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

2 + (2 + 4) ÷ 4 x 2 - 5²
P: 2 + (6) ÷ 4 x 2 - 5²
E: 2 + 6 ÷ 4 x 2 - 25
MD: 2 + \( \frac{6}{4} \) x 2 - 25
MD: 2 + \( \frac{12}{4} \) - 25
AS: \( \frac{8}{4} \) + \( \frac{12}{4} \) - 25
AS: \( \frac{20}{4} \) - 25
AS: \( \frac{20 - 100}{4} \)
\( \frac{-80}{4} \)
-20

To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{20}{64} \) = \( \frac{\frac{20}{4}}{\frac{64}{4}} \) = \( \frac{5}{16} \)

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

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

3\( \sqrt{9} \) x 6\( \sqrt{3} \)
(3 x 6)\( \sqrt{9 \times 3} \)
18\( \sqrt{27} \)

Now we need to simplify the radical:

18\( \sqrt{27} \)
18\( \sqrt{3 \times 9} \)
18\( \sqrt{3 \times 3^2} \)
(18)(3)\( \sqrt{3} \)
54\( \sqrt{3} \)

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