The addition rule for union is:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
You subtract P(A ∩ B) because outcomes in both A and B get counted twice when you add P(A) + P(B).
If P(A) = 1/2, P(B) = 1/3, and P(A ∩ B) = 1/6, then P(A ∪ B) = 1/2 + 1/3 - 1/6 = 2/3.