To solve the absolute value equation \(-3 - |6 - 3x| + 7 = 4\), we first simplify the equation.
Starting from the original equation:
\[
-3 - |6 - 3x| + 7 = 4
\]
We combine the constants \(-3\) and \(7\):
\[
4 - |6 - 3x| = 4
\]
Next, we isolate the absolute value term:
\[
-|6 - 3x| = 0
\]
This implies:
\[
|6 - 3x| = 0
\]
An absolute value is equal to zero when its argument is zero:
\[
6 - 3x = 0
\]
Solving for \(x\):
\[
3x = 6 \implies x = 2
\]
Next, we check if \(x = 2\) is a solution by substituting it back into the original equation:
\[
-3 - |6 - 3(2)| + 7 = 4
\]
Calculating the absolute value:
\[
6 - 6 = 0 \implies |6 - 3 \cdot 2| = 0
\]
Thus, we have:
\[
-3 - 0 + 7 = 4
\]
\[
4 = 4
\]
Since this is true, the solution is confirmed to be correct.
Thus, the solution is:
\[
\boxed{2}
\]