A translation is a rigid motion which preservers length and angle measures. This means that GH and G'H' are going to be parallel to each other.
Note that if we connect G with G' and H with H', these segments are parallel. This is because the translation of GH to G'H' moves the endpoints the same number of units in the vertical and horizontal directions. In other words, the lines have the same slope and thus they are parallel.
We can conclude that the resulting quadrilateral is a parallelogram.
Extra
The image may not be a quadrilateral
We saw in this solution that, if GG'H'H is a quadrilateral, then it is a parallelogram. There is a case in which we do not obtain a quadrilateral. Consider the case where the direction of the translation is parallel to GH. For example, let GH be a horizontal segment. Let's perform a horizontal translation.
We see above that we do not obtain a quadrilateral by performing a translation parallel to the segment
