Simplity: `(x+6) (x+4) (x-2)`

Answer

To simplify the expression \((x + 6)(x + 4)(x - 2)\), we will follow these steps:

### Step 1: Multiply the first two brackets
We start by multiplying the first two expressions, \((x + 6)\) and \((x + 4)\).

\[ (x + 6)(x + 4) = x^2 + 4x + 6x + 24 = x^2 + 10x + 24 \]

### Step 2: Multiply the result with the third bracket
Now, we take the result from Step 1, which is \((x^2 + 10x + 24)\), and multiply it by the third expression \((x - 2)\).

\[ (x^2 + 10x + 24)(x - 2) \]

We will distribute each term in the first bracket by each term in the second bracket:

1. Multiply \(x^2\) by each term in \((x - 2)\):
\[ x^2 \cdot x = x^3 \]
\[ x^2 \cdot (-2) = -2x^2 \]

2. Multiply \(10x\) by each term in \((x - 2)\):
\[ 10x \cdot x = 10x^2 \]
\[ 10x \cdot (-2) = -20x \]

3. Multiply \(24\) by each term in \((x - 2)\):
\[ 24 \cdot x = 24x \]
\[ 24 \cdot (-2) = -48 \]

### Step 3: Combine all the terms
Now, we combine all the results from the multiplications:

\[ x^3 + (-2x^2 + 10x^2) + (-20x + 24x) - 48 \]

This simplifies to:

\[ x^3 + 8x^2 + 4x - 48 \]

### Final Result
Thus, the simplified expression is:

\[ \boxed{x^3 + 8x^2 + 4x - 48} \]

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