To determine the value of \( h \) in the function \( f(x) = x + h \) that describes the translation of the point from \( (5, 6) \) to \( (3, 6) \), we need to focus on the \( x \)-coordinates.
The original \( x \)-coordinate is 5, and the new \( x \)-coordinate after translation is 3. Thus, we can express this translation mathematically as:
\[ f(5) = 3 \]
Substituting into the function gives:
\[ 5 + h = 3 \]
To find \( h \), we solve the equation:
\[ h = 3 - 5 = -2 \]
Therefore, the value of \( h \) is \(-2\).