Writing two column proofs

You have the right idea so far.

Use the fact that x = y and z = y to get x = z. We can use the transitive property or the substitution property (they are effectively the same idea).

Then you'll use the fact that w = x and w = t to get x = t. The same property is used here as well.

Lastly, connect x = z and x = t which will end up with t = z.