How to Design Binary Multiplier for 2 bits?
Think. You learned the on-paper multi-row method of decimal multiplication? Just transfer that to binary. All you need is addition (HA and FA) and multiplication (AND, but a suitably wired MUX will do fine). Your teacher was mild, in the assignement below I ask for a 4 x 4 multiplier :) The text it Dutch, but it might give you some hints. It also show  a block diagram of an 8 x 8 multiplier.

http://www.voti.nl/hvu/1ICSN1/2004-2005-1ICSN1-5-p.doc