Does this solution make sense to anyone? It looks like we have a Common Source amp followed by a Common Gate amp. But the solution seems to indicate otherwise.

 

Your never heard about cascode amplifier?
http://en.wikipedia.org/wiki/Cascade_amplifier

 

I have but I'm not seeing how this specific example is worked.

 

Hmm, solution look good.
And I gave the wrong link, here is a correct link
http://en.wikipedia.org/wiki/Cascode
M1 and M2 is a cascode amplifier and M3 acts as a active load.