You know that m<TSU=m<PSR because they make a vertical angle pair.
So...m<PSR=4x.
If, m<QSR=3x then m<PSQ=4x-3x=x because they are adjacent.
And, m<PQS=180-68=112 degrees (linear pair).
Now we know all the interior angles in triangle PQS so we can say that...
x+x+112=180 (sum of interior angles in triangle)
2x=68
x=34 degrees
