this problem was solved incorrectly, solve the problem correctly then explain the error made:

Let's solve the equation correctly step by step.

The original equation is:

\[ 3x + 2x - 6 = 24 \]

1. First, combine like terms on the left side:

   \[ (3x + 2x) - 6 = 24 \] \[ 5x - 6 = 24 \]

2. Next, add 6 to both sides to isolate the term with \(x\):

   \[ 5x - 6 + 6 = 24 + 6 \] \[ 5x = 30 \]

3. Now, divide both sides by 5 to solve for \(x\):

   \[ x = \frac{30}{5} \] \[ x = 6 \]

So the correct solution is \(x = 6\).

Explanation of the Error:

1. The first error occurs in the step where \(-2x - 2x\) was performed. It appears the equations were either incorrectly manipulated or miswritten.

2. The subsequent step where \(x - 6 = 24\) was written is incorrect; it seems to have dropped some terms and made an arbitrary simplification that did not follow the rules of algebra.

3. The final calculation mistakenly suggested adding 6 to both sides to get \(x = 30\) instead of recognizing that \(5x = 30\) must be divided by 5 to find \(x\).

The proper steps consistently follow arithmetic operations, and the use of parentheses to ensure each step is clear and accurate would help avoid such errors.