The outcomes are all the different ways we can draw a ticket from F and another from G. As a shorthand, let's write 00 to mean the ticket from F has a 0 and the ticket from G has a 0. The outcomes then are 00, 01, 10, and 11.
A box model for F # G therefore has four outcomes. They are equally likely: this is what being independent really means.
Consequently, we should put four tickets in the F # G box. On them are written 00, 01, 10 and 11.
Because there are four tickets, each ticket has a probability of 1/4 = 25% of being drawn.
You should recognize this as the B(2, 1/2) box introduced in problem 3. We can write
B(1, 1/2) # B(1, 1/2) = B(2, 1/2).