Although you don’t say so, it’s usual in this type of puzzle for each different letter to indicate a different digit.
We can immediately see that R=1, because R x WE = WE.
We can also see that E x E must end in Y. Taking all the numbers from 0 to 9 and squaring them, we can eliminate 0, 1, 5 and 6 because their squares end in the same digits as the original numbers. We can also eliminate 9, because its square ends in 1, which has already been used for R.
This leaves 2, 3, 4, 7 and 8 as possibilities for E, giving 4, 9, 6, 9 and 4 respectively for Y.
We can also note that W x E (plus any number carried forward from E x E) must equal Y. After some trial and error, the only possibility is E=8, Y=4 and W=6, which implies that A=5.
This is enough to complete the calculation, showing 68 x 518 = 35,224, and therefore H=3, P=2 and Z=0.