How to multiply using gates?
I'm having a hard time trying to understand the schematic...however: there are several different architectures for binary multipliers, but all of them are based on simple considerations.

1- The multiplication in binary logic is made by the AND operator. Therefore you will need a battery of AND gates that multiply each bit of one factor for each bit of the other.

To make it simpler, let's call the factors A and B, of M and N bits respectively. The AND product of the two numbers will give N vectors of M bits, with increasing weight. Now you have to sum up all the vectors considering the weight of each one, to obtain the result.

Long story short: I see the full adders, but you first miss the AND operators.

Some more info on wiki.