Circle

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