3-bit full adder, how can you solve this problem?

First, an example of what the task is about:

For example, we have two 2-bit binary numbers: y1y0 and x1x0, so y1 is one bit, y0 too, the same for x1 and x0, together these are two 2-bit numbers.

Now we should calculate the product: y1y0*x1x0, which is trivially:

However, it must be noted that y0x0, y0x1, etc. should have been connected by an AND gate before input, which was not done here because it is trivial.

The solution becomes clear when you :

observed.

NOW: I could still think of that, but now the task becomes more complex:

How can one depict such a product?