To simplify the expression \(4 + 8(3x - 2) - 7x\), we first apply the distributive property to the term \(8(3x - 2)\):
\[ 8(3x) - 8(2) = 24x - 16. \]
Now, substitute this back into the expression:
\[ 4 + 24x - 16 - 7x. \]
Next, combine like terms. The constant terms \(4 - 16\) simplify to \(-12\), and the \(x\) terms \(24x - 7x\) simplify to \(17x\):
\[ -12 + 17x. \]
Thus, the simplified expression is:
\[ 17x - 12. \]