Let's simplify the expression \( (7x + 6) - (8 + x) \).
Start by distributing the negative sign to the terms inside the parenthesis:
\[ (7x + 6) - (8 + x) = 7x + 6 - 8 - x \]
Now, combine the like terms:
- Combine the \( x \) terms: \( 7x - x = 6x \)
- Combine the constant terms: \( 6 - 8 = -2 \)
Putting it all together, we get:
\[ 6x - 2 \]
Therefore, the simplified expression is:
\[ \boxed{6x - 2} \]