Let the width of the rectangle be denoted as \( w \) meters. According to the problem, the length \( l \) can be expressed as:
\[ l = 2w - 4 \]
The area of the rectangle \( A \) is given by the formula:
\[ A = l \times w \]
Substituting the expression for \( l \) into the area formula, we get:
\[ 96 = (2w - 4) \times w \]
Expanding this equation, we have:
\[ 96 = 2w^2 - 4w \]
Rearranging the equation to set it to zero gives:
\[ 2w^2 - 4w - 96 = 0 \]
Dividing the entire equation by 2 simplifies it:
\[ w^2 - 2w - 48 = 0 \]
Next, we can factor the quadratic equation:
\[ (w - 8)(w + 6) = 0 \]
Setting each factor equal to zero gives us:
\[ w - 8 = 0 \quad \text{or} \quad w + 6 = 0 \]
Thus, we have:
\[ w = 8 \quad \text{or} \quad w = -6 \]
Since a width cannot be negative, we discard \( w = -6 \) and accept \( w = 8 \).
Now, substituting back to find the length:
\[ l = 2w - 4 = 2(8) - 4 = 16 - 4 = 12 \]
Therefore, the dimensions of the rectangle are:
- Width: \( 8 \) meters
- Length: \( 12 \) meters
In conclusion, the length and width of the rectangle are:
\[ \text{Length} = 12 \text{ m}, \quad \text{Width} = 8 \text{ m} \]