In a school that has 20 teachers, 10 teach mathematics, 8 teach social studies, and 6 teach science. two teach both mathematics and social studies, but none teach both social studies and science. how many teach both mathematics and science?

2

In this school the number of teachers would be:
Mathematics(M) = 10
Social Studies (SS)= 8
Science(S)= 6
Total teacher= 20

Two teach both Mathematics and Social Studies
M∩SS= 2
none teach both Social Studies and Science
SS∩S= 0

Using the calculation for the total teacher you can determine M∩S:
Total teacher= M + SS + S - M∩SS - M∩S - SS∩S
Total teacher= M + SS + S - M∩SS - M∩S - SS∩S
20= 10+8+6 -2 - M∩S -0
20= 22- M∩S 
M∩S = 22=20= 2