In order to find the length of MQ, we can first draw a segment from the intersection point of the diagonals (let's call it D) and parallel to sides NM and PQ, going down to point K, like this:
The segment DK has a length of half the length of PQ, so we have DK = 2.
Now, we can use the Pythagorean Theorem to find the length of KQ:

The length of KQ is half the length of MQ, so we have:

Rounding to the nearest tenth, we have MQ = 9.2 units