To simplify the expression \(5a - 8c + b + 3c - 9a + 6b\), we will combine like terms.
First, let's group the terms involving \(a\), \(b\), and \(c\):
- For \(a\): \(5a - 9a = -4a\)
- For \(b\): \(b + 6b = 7b\)
- For \(c\): \(-8c + 3c = -5c\)
Now, we can write the simplified expression by combining these results:
\[ -4a + 7b - 5c \]
Thus, the simplified form of the expression is
\[ \boxed{-4a + 7b - 5c} \]