In the figure below side AB of triangle ABC constrains which point?...

Add in point D that is directly below point B, such that point D is on the x axis. The distance from A to D is 9 units and you can use the pythagorean theorem to find this. The slope of line AB is 12/9 = 4/3, meaning the equation of the line that goes through points A and B is y = (4/3)x

Through trial and error, you'll find that point (6,8) is on the line y = (4/3)x

Alternatively note how y/x = 4/3 when (x,y) = (9,12) and when (6,8) also.