Let June's age be \( x \). Then, Kevin's age would be \( x + 4 \) since he is four years older than June.
According to the problem, the sum of their ages is 14:
\[ x + (x + 4) = 14 \]
Simplifying the equation:
\[ 2x + 4 = 14 \]
Subtracting 4 from both sides:
\[ 2x = 10 \]
Dividing by 2:
\[ x = 5 \]
So, June is 5 years old. Therefore, Kevin's age is:
\[ x + 4 = 5 + 4 = 9 \]
Thus, Kevin is 9 years old.