Answer
$(9a,7b)$
Work Step by Step
Step 1. Assume the coordinates of the other endpoint are $(x,y)$
Step 2. Use the formula for midpoint, we have $\frac{x+(3a)}{2}=6a$ and $\frac{y+5b}{2}=6b$
Step 3. Solve above equations to get $x=9a, y=7b$, thus the other endpoint is $(9a,7b)$