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