A research study found that, of 500 people surveyed, 220

Here are the two formulas

1. [Total = Group1 + Group2 - Both + Neither]

Used when Group1 includes Both.
e.g. given 160 people watch network A. This means 160 watch network A and it includes those people who watch both the networks. Similarly, Group2 includes people who watch both the networks e.g. given 160 watch network B - 160 includes the number of people who watch both networks.
Since no of people who watch both networks is included twice, you subtract it out once.

500 = 160 + 160 - 40 + 220

2. [Total = Group1 + Group2 + Both + Neither]

Used when Group1 is the number of people who watch ONLY network A
e.g. given 120 people watch ONLY network A (compare this with above where the word ONLY is missing). Group2 includes people who watch ONLY network B. Since you haven't accounted for the people who watch both, you add Both once.

500 = 120 + 120 + 40 + 220

Hope both the formulas make sense now.

Here, you are given that 120 watched only network A so you use the second formula. Also, it might be a good idea to get comfortable with venn diagrams. Such confusions do not occur if you always use the venn diagram.