To solve the inequality \(3x - 8 > 4x - 12\), we will follow these steps:

1. First, let's isolate the variable \(x\). We can start by eliminating \(4x\) from both sides:

\[
3x - 8 - 4x > -12
\]

This simplifies to:

\[
-1x - 8 > -12
\]

2. Next, we can add \(8\) to both sides to isolate the term with \(x\):

\[
-1x > -12 + 8
\]

This simplifies to:

\[
-1x > -4
\]

3. To solve for \(x\), divide both sides by \(-1\). Remember that when you divide or multiply both sides of an inequality by a negative number, you must switch the direction of the inequality:

\[
x < 4
\]

So, the solution to the inequality \(3x - 8 > 4x - 12\) is:

\[
x < 4
\]

This means that \(x\) can take any value less than 4.