Let's denote June's age as \( J \). According to the information provided, Kevin is 4 years older than June, so we can express Kevin's age as \( K = J + 4 \).
The problem states that the sum of their ages is 14:
\[ K + J = 14 \]
Substituting \( K \) with \( J + 4 \):
\[ (J + 4) + J = 14 \]
This simplifies to:
\[ 2J + 4 = 14 \]
Now, subtract 4 from both sides:
\[ 2J = 10 \]
Dividing both sides by 2 gives:
\[ J = 5 \]
Now, we can find Kevin's age:
\[ K = J + 4 = 5 + 4 = 9 \]
So, Kevin is 9 years old.