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'(6 + 3, 5 - 2) = \boxed{(9, 3)} $.