To solve the inequality \((x - 5)/4 - (x + 1)/3 > 2\), you can follow these steps:

1. Find a common denominator for the fractions, which in this case is 12.

2. Multiply both sides of the inequality by 12 to eliminate the fractions:

\[(12/4) * (x - 5) - (12/3) * (x + 1) > 2 * 12\]

3. Simplify the equation:

\[3(x - 5) - 4(x + 1) > 24\]

4. Distribute the constants:

\[3x - 15 - 4x - 4 > 24\]

5. Combine like terms:

\[-x - 19 > 24\]

6. Add 19 to both sides of the inequality:

\[-x > 43\]

7. Finally, multiply both sides by -1, but remember that when you multiply or divide by a negative number, you must reverse the inequality sign:

\[x < -43\]

So, the solution to the inequality is \(x < -43\).