Need
a figure is reflected across two parallel lines separated by 8 inches. it is then reflected across one line first, and then the other. how far is the figure translated?

  twice the distance between the lines

Step-by-step explanation:

The first image is a distance from the original that is twice the distance to the first line of reflection. The second image is a distance from the first image that is twice the distance from the first image to the second line of reflection.

Suppose the original is at the origin, and the first line of reflection is at distance "a". Then the first image is at 2a. If the second line of reflection is at "b", the location of the second image is 2b -2a = 2(b -a).

The second reflected image is translated from the original by twice the distance between the lines of reflection. The direction of translation is in the direction of the second line of reflection from the first.

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Note that this holds regardless of the signs or magnitudes of "a" and "b".