I think perhaps r1c3 of your grid should contain 1 rather than 7:
421 3XX X9X
X7X 489 231
893 612 574
748 9X3 12X
1X9 24X 3XX
X32 8X1 94X
2X7 534 X19
91X 728 4X3
3X4 196 7X2
If you look at columns 2 and 8, only two cells in each can accommodate 6. They are marked with an asterisk:
421 3XX X9X
X7X 489 231
893 612 574
748 9X3 12X
1*9 24X 3*X
X32 8X1 94X
2*7 534 X19
91X 728 4*3
3X4 196 7X2
As they line up in row 5 and row 5 can contain only one 6, one of r7c2 and r8c8 must contain a 6. You don’t know which but, however it turns out, 6 may be eliminated from any cell which is associated with both r7c2 and r8c8. Thus it can be eliminated from r7c7 and r8c3, which solves the puzzle.
This configuration is known as an x-wing. You can read about it
here.
Steve