18
Let us solve this question by denoting variables.
Nice afternoons = P
Nice mornings = Q
No rain = R
Now, the number of days with rain = P + Q = 13
Days with clear mornings = Q + R = 11
Days with clear afternoons = P + R = 12
If we solve these three equations, we will get:
P = 7
Q = 6
R = 5
The total number of days = P + Q + R = 18