To simplify the expression \( 10z - 4z + z + 4 - 4z \), you can combine like terms.
First, combine the terms with \( z \):
\[ 10z - 4z + z - 4z \]
Combine the coefficients:
\[ (10 - 4 + 1 - 4)z = (10 - 4 - 4 + 1)z = (10 - 8)z = 2z \]
So, the \( z \) terms simplify to \( 2z \).
Now, add the constant term:
\[ 2z + 4 \]
Thus, the simplified expression is:
\[ \boxed{2z + 4} \]