To multiply terms with radicals, multiply the coefficients and radicands separately:

8\( \sqrt{4} \) x 2\( \sqrt{6} \)
(8 x 2)\( \sqrt{4 \times 6} \)
16\( \sqrt{24} \)

Now we need to simplify the radical:

16\( \sqrt{24} \)
16\( \sqrt{6 \times 4} \)
16\( \sqrt{6 \times 2^2} \)
(16)(2)\( \sqrt{6} \)
32\( \sqrt{6} \)

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

4 + (2 + 2) ÷ 3 x 2 - 2²
P: 4 + (4) ÷ 3 x 2 - 2²
E: 4 + 4 ÷ 3 x 2 - 4
MD: 4 + \( \frac{4}{3} \) x 2 - 4
MD: 4 + \( \frac{8}{3} \) - 4
AS: \( \frac{12}{3} \) + \( \frac{8}{3} \) - 4
AS: \( \frac{20}{3} \) - 4
AS: \( \frac{20 - 12}{3} \)
\( \frac{8}{3} \)
2\(\frac{2}{3}\)

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-8x^5}{5x^4} \)
\( \frac{-8}{5} \) x^{(5 - 4)}
-1\(\frac{3}{5}\)x

By buying two shirts, Charlie will save $25 x \( \frac{40}{100} \) = \( \frac{$25 x 40}{100} \) = \( \frac{$1000}{100} \) = $10.00 on the second shirt.

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 18 meters so the equation becomes: 2w + 2h = 18.

Putting these two equations together and solving for width (w):

2w + 2h = 18
w + h = \( \frac{18}{2} \)
w + h = 9
w = 9 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 9 - 2w
3w = 9
w = \( \frac{9}{3} \)
w = 3

Since h = 2w that makes h = (2 x 3) = 6 and the area = h x w = 3 x 6 = 18 m²