Maybe this will help:
First notice that the voltage at Q4 emitter is
Ve = Ix * (Re4||(hie+Ry)) and if substitute Rx = (Re4||(hie+Ry)) we have Ve = Ix*Rx
Next we notice that I_hoe = Ix - (-Ib*hfe) and Ib is (Ix*Rx)/hie we have our KVL equation
Vx = Ix*Rx + [Ix - ((-Ix*Rx)/hie*hfe)]*hoe
And now all you need is to do it solve for Ix and Ro = 1/Ix
First notice that the voltage at Q4 emitter is
Ve = Ix * (Re4||(hie+Ry)) and if substitute Rx = (Re4||(hie+Ry)) we have Ve = Ix*Rx
Next we notice that I_hoe = Ix - (-Ib*hfe) and Ib is (Ix*Rx)/hie we have our KVL equation
Vx = Ix*Rx + [Ix - ((-Ix*Rx)/hie*hfe)]*hoe
And now all you need is to do it solve for Ix and Ro = 1/Ix