jmc

When an image is translated to the right we just add the number of units it is being translated to the original $x$-coordinate. When an image is translated down we just subtract that number of units from the $y$-coordinate. In this case we'll subtract 2 from the $y$-coordinates and add 3 to the $x$-coordinates. This will make point $B(6,5)$ move to $B^{\prime }(6+3,5-2)=\boxed{(9,3)}$.