To find the explanation of the translation using the rule (x,y) (x-4, y+2) you need to know what a translation is.
A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.
The x is on the horizontal axis, so your moving -4 quadrants to the left.
The y is on the vertical axis, so your moving 2 upwards.
So, you would move -4 left, and 2 upwards.