To simplify the expression \( 9g - 7h - 6g + 2h \), we can combine like terms.
First, combine the \( g \) terms:
\[ 9g - 6g = 3g \]
Next, combine the \( h \) terms:
\[ -7h + 2h = -5h \]
Putting it all together, we have:
\[ 3g - 5h \]
So, the simplified expression is \( \boldsymbol{3g - 5h} \).