To simplify the expression \( 5a - 8c + b + 3c - 9a + 6b \), we combine like terms.
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Combine the \( a \) terms: \( 5a - 9a = -4a \)
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Combine the \( c \) terms: \( -8c + 3c = -5c \)
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Combine the \( b \) terms: \( b + 6b = 7b \)
Putting it all together, we have:
\[ -4a - 5c + 7b \]
Thus, the simplified expression is \( -4a + 7b - 5c \).