Completing 64o from the small blind is the only real leak here; postflop we just give up with total air on a board that smashes BB’s range.
Flop 9c 7c Ks, BB checks and we have pure nothing with 6d4s, out of position and not the preflop aggressor. This board connects very naturally with BB’s checking range (any Kx, 9x, 7x, a bunch of club draws and gutshots), while we show up with a lot of total junk. Checking back and essentially giving up with 6‑high is standard—leading as a bluff here is too thin, especially with no clubs and only a backdoor gutshot to a 5.
Turn 3c brings the third club, BB checks again. The board is now 9c 7c Ks 3c and we still have 6d4s: 6‑high, no club, and just a gutshot to a 5. The turn heavily favors BB’s range in theory—lots of their random club holdings and Kx/9x now have strong made hands or good draws. Bluffing here with our exact combo is unattractive: we don’t block any strong value (no K, 9, 7, or club), and we also don’t block folds (random Q-high/J-high without a club). Checking and continuing to give up is correct.
River pairs the 9: board 9c 7c Ks 3c 9s, BB checks and we still have 6‑high with no relevant blockers. BB can easily have a 9, Kx, some flushes, or even stubborn A‑high that won’t fold to a single river stab in a limped pot. As a bluff candidate, 6d4s is very poor—we don’t block better folds like A-high with a club, nor do we block the obvious calls. Checking and surrendering the pot is fine; the main leak in the hand happened before the flop, not here.