To simplify the expression \(-34r + 3 - 56r - 6\), we can combine like terms.
First, combine the \(r\) terms: \[ -34r - 56r = -90r \]
Next, combine the constant terms: \[ 3 - 6 = -3 \]
Putting it all together, the simplified expression is: \[ -90r - 3 \]
So, the final answer is: \[ \boxed{-90r - 3} \]