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