Stackelberg Oligopoly 3 firms Imagine that there are 3 firms in a monopolistic market, F1, F2 and F3. Firms 1 and 2 are incumbent firms and act simultaneously whereas Firm 3 observes the actions of both firms before deciding whether to enter. 

All firms face a market price of $P(Q) = 16-q_1-q_2-q_3$. Incumbent firms face a production cost of $C_i (q_i) = 4q_i$ for $i= 1,2$. Firm 3 faces a production cost of $C_3(q_3) = 4 + 4q_3$. Find both firm 3 and firm 1's payoff.

I understand that I need to take firm 3's best response function which is 
$$0.5  (12-q_2-q_1)$$ 
but I am not sure where to go from there. Do I substitute this back into the price equation? I tried doing this but it wouldn't yield any definitive answers. Thanks!
You are right that you first have to find F3's best-response function. F1 and F2 take as given this reaction of F3 to whatever they produce.
Hence, you plug this best-response function into the incumbents' profit maximization problem. In that way, you take care of the fact that the incumbents anticipate F3's reaction, indirectly determining $q_3$.

You should also check if the resulting reaction quantity $q_3$ is non-negative! It can be optimal to deter the entry of F3 completely.