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