Sets
The question defines two sets where people can be or not:
P = People that play piano
G = People that play guitar
The music club has a total of 20 members out of which 4 don't play piano nor guitar. So, from the total number of members, we are sure 16 people play either piano or guitar or maybe both of them.
We know 12 people played piano and 11 played guitar. We already know there are 16 people in both sets, so how is it possible to have 12+11=23 people playing piano or guitar?
The answer is: because there are 23 - 16 = 7 people playing both instruments.
To summarize:
7 people play piano and guitar
12 - 7 = 5 people play only piano
11 - 7 = 4 people play only guitar
4 do not play any of those.
That gives us the required total of 7 + 5 + 4 + 4 = 20 people7 people play piano and guitar