The defense has found your weak spot, so you must now take the next eight tricks on the run. You have four easy diamond tricks, of course, so you need to play the club suit for four tricks, too. That means the ♣K must be onside for you to make the contract, but some care is required even if the finesse is working.
It would be poor to play the ♣2 to dummy’s queen (or 10). When the finesse works, you’d have no way back to your hand to repeat it without the defense running the spade suit.
The ♣J looks better, and many players would reflexively choose it, but it, too, would be a mistake. Say this is the layout:
After winning the ♠A, say you run the ♣J, playing the ♣3 from dummy. The lead is still in your hand. When you take the finesse again, you’ll be stuck in dummy.
You need to be able to finesse in clubs three times, and the only way to do that against this layout is to start with the ♣9, playing low from dummy if West refuses to cover. Next, run the ♣J, on which you will play dummy’s ♣10 if West ducks. Finally, you’ll play the ♣2 to dummy’s queen.
