Since OX meets chord MN at right angles, it bisects MN....so XN = 6
And OY meets chord PQ at right angles, so it bisects PQ.
And since OX = OY....chords MH and PQ are equidistant from the center of the circle. And chords that are equidistant from the center of a circle have the same length.
So PQ = 12.....so YQ = 6