What are the variables if pt= 2x, tr= y+4, qt= x+2, ts=y

The missing aspect of this question is shown in the attached image, which is that the letters correspond to vertices of a parallelogram.

A key feature of the parallelogram is that the diagonals bisect each other, therefore:

PT = TR
QT = TS

With this information we can now plug in the equations and solve for the variables x and y.

PT = TR
2x = y+4
y = 2x - 4

QT = TS
x + 2 = y

We now have two equations for the variable y. With this we can solve for x.

2x - 4 = x + 2
x = 6

y = x + 2
y = 6 + 2
y = 8

Once we solved for the variable x, we simply placed that value back into one of the previous equations and solved for y. The results are x = 6, y = 8.