Note that when translating right or left, you are actually changing the x.
Translating right, means that you are adding 4 to the x.
When: (x , y) = (-3 , -4), and you are translating to the right 4 units
(-3 + 4, -4)
simplify
(1, -4)
P'(1, -4) is the coordinates for it's image
hope this helps