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Need help to figure out on how to proceed

Just by eyeballing I can see a Skyscraper in 6s with strong links on rows 3 and 8. That eliminates 6 from r1c5 and r9c4. I don’t know if it solves the puzzle but it should help. (I’m just looking at it on my phone so can’t analyze any further right now.)

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*--------------------------------------------------------------------------------*
| 23      1      a68       | 9      b68      23       | 4       5       7        |
| 38      9       7        | 5       4       38       | 2       6       1        |
| 5       2-6     4        | 26      17      17       | 3       8       9        |
|--------------------------+--------------------------+--------------------------|
| 2489    2458    3        | 7       5689    689      | 589     1       24       |
| 1       7       589      | 48      2       489      | 589     3       6        |
| 6       24      589      | 3       1589    189      | 589     7       24       |
|--------------------------+--------------------------+--------------------------|
| 478     458     1        | 248     3       2478     | 6       9       58       |
| 89     d368     2        | 1      c689     5        | 7       4       38       |
| 4789    34568   589-6    | 468     6789    46789    | 1       2       358      |
*--------------------------------------------------------------------------------*

Here is another Skyscraper on 6's in the diagram, In cells a-b-c-d. One of cells a or d must be True in the solution, so the pattern eliminates the 6's in r3c2 & r9c3 and the puzzle solves easily from there.

If you don't know about Skyscrapers you can read about them here.

Leren

I'm finally at my computer, so let's take a bit deeper look. Looks like the Skyscraper I saw earlier does solve the puzzle, so I got lucky. Leren showed another one, and there's still one more available (try to find it yourself!).

There are also several other single-digit patterns (2-String Kites etc.) with the same effect. All of them on digit 6. (Well, there's one pattern with 8s but it doesn't help.)

However, there's a bit of a problem with your pencil marks that needs to be addressed first:

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.-------------------.------------------.-------------.
| 23    1      68   | 9    68    23    | 4    5  7   |
| 38    9      7    | 5    4     38    | 2    6  1   |
| 5     26     4    | 26   17    17    | 3    8  9   |
:-------------------+------------------+-------------:
| 2489  2458   3    | 7    5689  689   | 589  1  24  |
| 1     7      589  | 48   2     489   | 589  3  6   |
| 6     24-58  589  | 3    1589  189   | 589  7  24  |
:-------------------+------------------+-------------:
| 478   458    1    | 248  3     2478  | 6    9  58  |
| 89    368    2    | 1    689   5     | 7    4  38  |
| _7_9  34568  5689 | 468  6789  46789 | 1    2  358 |
'-------------------'------------------'-------------'

How did you eliminate 4 and 8 from r9c1? Neither is a basic elimination at this point, and one is incorrect. You won't be able to solve the puzzle until you fix that.

You also seem to have missed one basic technique. There's a Hidden Pair (24) in row 6, so you can eliminate 58 from r6c2. It actually doesn't make a difference, but just so you know.

The correct pencil marks after basics (same as in Leren's post):

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.--------------------.------------------.-------------.
|  23    1      68   | 9    68    23    | 4    5  7   |
|  38    9      7    | 5    4     38    | 2    6  1   |
|  5     26     4    | 26   17    17    | 3    8  9   |
:--------------------+------------------+-------------:
|  2489  2458   3    | 7    5689  689   | 589  1  24  |
|  1     7      589  | 48   2     489   | 589  3  6   |
|  6    *24     589  | 3    1589  189   | 589  7  24  |
:--------------------+------------------+-------------:
|  478   458    1    | 248  3     2478  | 6    9  58  |
|  89    368    2    | 1    689   5     | 7    4  38  |
| *4789  34568  5689 | 468  6789  46789 | 1    2  358 |
'--------------------'------------------'-------------'

The two cells that are different from yours are r6c2 and r9c1. The former doesn't matter, but the latter needs to be fixed.

Starting from Leren's PM:

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(solve-sukaku-grid
   *--------------------------------------------------------------------------------*
   ! 23      1       68       ! 9       68      23       ! 4       5       7        !
   ! 38      9       7        ! 5       4       38       ! 2       6       1        !
   ! 5       26      4        ! 26      17      17       ! 3       8       9        !
   !--------------------------+--------------------------+--------------------------!
   ! 2489    2458    3        ! 7       5689    689      ! 589     1       24       !
   ! 1       7       589      ! 48      2       489      ! 589     3       6        !
   ! 6       24      589      ! 3       1589    189      ! 589     7       24       !
   !--------------------------+--------------------------+--------------------------!
   ! 478     458     1        ! 248     3       2478     ! 6       9       58       !
   ! 89      368     2        ! 1       689     5        ! 7       4       38       !
   ! 4789    34568   5896     ! 468     6789    46789    ! 1       2       358      !
   *--------------------------------------------------------------------------------*
)

A mere finned x-wing will do the job:

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***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin
***  Using CLIPS 6.32-r770
***********************************************************************************************
121 candidates, 552 csp-links and 552 links. Density = 7.6%
finned-x-wing-in-columns: n6{c4 c3}{r9 r3} ==> r3c2 ≠ 6
stte


denis_berthier wrote:A mere finned x-wing will do the job

Are you implying that's a simpler pattern than the two Skyscrapers that have been presented? Well...

finned-x-wing-in-columns: n6{c4 c3}{r9 r3} ==> r3c2 ≠ 6

More accurately that's a Finned Sashimi X-Wing, with a Siamese twin that would eliminate 6r1c5. Most people would call such a pattern Skyscraper. It's the third available Skyscraper I mentioned earlier.

There's a non-sashimi Finned X-Wing (Grouped Skyscraper) right next to it:

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Finned X-Wing: (6)c24\r39b7 => -6 r9c3; stte

That was actually the first pattern I spotted, but I chose to report the Skyscraper because many would consider it simpler. It's probably a wash, actually, because the relative simplicity depends on one's point of view. This one would be easier to spot as a fish (being non-sashimi), but harder as a chain (being grouped).