When you translate figures in the coordinate system, any horizontal movemets are done by modifying the values over the X-axis and the vertical movements are done by modifying the values over the Y-axis.
The points were only moved, but the figure was not modified, this means that the constants were added/subtracted from the original coordinates.
When it was moved to the right 3 places, it means that they added 3 to each X-coordinate.
The movement down 2 places means that it was subtracted 2 to each Y-coordinate.
A(-1,0) → A''((-1+3),(0-2)) → A''(2,-2)
B(3,2) → B'' ((3+3),(2-2)) → B'' (6,0)
C(4,5) → C''((4+3),(5-2)) → C''(7,3)