Making a circuit entirely with 4:1 MUX, 2-input OR gate and NOT gate
So you need to OR some ANDs. Reserve the OR for that.
And you need Y', so use the inverter for that.
Now  you need X, and YZ.
Can the 4:1 mux do that?
=================================
The MUX has 4 + 2 = 6 inputs. Draw a truth table.
Given the MUX has only ONE output pin, can the MUX generate X + YZ?
If not, then we need to reconsider.