The length of a rectangle is four meters less than twice its width.

Let's break down the problem step-by-step.

### Step 1: Set up expressions
1. **Length in terms of Width:**
According to the first statement, "The length of a rectangle is four meters less than twice its width."
We can express the length \( l \) in terms of the width \( w \) as:
\[ l = 2w - 4 \]

**So, the expression for the length of the rectangle in terms of the width would be:**
**l = 2w - 4**

2. **Formula for the Area of a Rectangle:**
The area \( A \) of a rectangle is calculated using the formula:
\[ A = l \times w \]

**So, the formula for the area of a rectangle is:**
**area = l x w**

### Step 2: Solve for dimensions
We are given that the area of the rectangle is 96 m². We can substitute the expression for the length into the area formula:
\[ A = (2w - 4) \times w \]
Setting the area equal to 96 m² gives us:
\[ (2w - 4) \times w = 96 \]
Expanding this:
\[ 2w^2 - 4w = 96 \]
Rearranging to set it to zero:
\[ 2w^2 - 4w - 96 = 0 \]
Dividing the entire equation by 2:
\[ w^2 - 2w - 48 = 0 \]

### Step 3: Factor the quadratic equation
To solve this quadratic equation, we can factor it:
\[ (w - 8)(w + 6) = 0 \]
Setting each factor to zero gives solutions:
1. \( w - 8 = 0 \) → \( w = 8 \) (valid since width must be positive)
2. \( w + 6 = 0 \) → \( w = -6 \) (not valid since width cannot be negative)

### Step 4: Find the Length
Now that we have \( w = 8 \):
Using the expression we derived for \( l \):
\[ l = 2w - 4 = 2(8) - 4 = 16 - 4 = 12 \]

### Final Dimensions
Thus, the dimensions of the rectangle are:
- **Width (w) = 8 m**
- **Length (l) = 12 m**

### Answer Summary
1. The expression for the length of the rectangle in terms of the width would be: **l = 2w - 4**
2. The formula for the area of a rectangle is: **area = l x w**
3. Using trial and error, if the area is 96 m², then the length and width are: **l = 12 & w = 8**.