(x+4)*(x+2)-(x-3)*(x+3)

To simplify the expression \((x+4)(x+2) - (x-3)(x+3)\), we'll start by expanding both products.

1. Expand \((x+4)(x+2)\): \[ (x + 4)(x + 2) = x^2 + 2x + 4x + 8 = x^2 + 6x + 8 \]

2. Expand \((x-3)(x+3)\): \[ (x - 3)(x + 3) = x^2 - 9 \quad \text{(This is a difference of squares)} \]

Now substitute these expanded forms back into the original expression: \[ (x^2 + 6x + 8) - (x^2 - 9) \]

3. Distribute the negative sign: \[ x^2 + 6x + 8 - x^2 + 9 \]

4. Combine like terms:

   • The \(x^2\) terms cancel each other out: \[ 6x + 8 + 9 = 6x + 17 \]

Thus, the simplified expression is: \[ \boxed{6x + 17} \]