A figure is translated using the rule (x,y). => (x-3,y+6)

So remember that the x-axis moves the coordinate horizontally (left and right), with the greater the x-coordinate the further right the coordinate is. And the y-axis moves the coordinate vertically (up and down), with the greater the y-coordinate the further up the coordinate is.
Looking at this translation in our problem, we decrease the x-coordinate by 3 and increase the y-coordinate by 6. Using what we know, this translation moves the figure 3 units to the left and up 6 units, or D.