With A6 on K-7-4-2-9cc and only ace-high plus a missed club draw, we should check and give up; bluffing runs into too many strong made hands and better club blockers.
On Kh-7d-4c rainbow, our range has a slight advantage but is still quite air-heavy. A6o with only ace-high and no real backdoors performs best as a check; if we do bet, a small 30% pot stab is preferred over the tiny 20% sizing we chose.
The 2c turn is a very low card that doesn’t change much for either range. Solver leans heavily toward checking here with A6o, as our hand has poor equity and doesn’t benefit from betting into a range that can continue with Kx, 7x, 4x, and some floats. The small 29% pot bet we chose is not the highest-EV line.
River 9c brings the third club and we still only have ace-high with a missed club draw. After betting flop and turn, our range is somewhat value-heavy, and BB can call with a wide range of Kx, 7x, 4x, 9x, and made flushes. With A6o we don’t block many of those strong hands and don’t have a strong bluff candidate, so checking and giving up is the best option.