Let the width of the rectangular garden be denoted by $w$ (in feet). According to the problem, the length is 8 feet longer than the width, so the length is $w + 8$ feet.

The perimeter $P$ of a rectangle is given by the formula: $P = 2 \times (\text{length} + \text{width})$ Substituting the given values: $196 = 2 \times ((w + 8) + w)$ Simplifying the equation: $196 = 2 \times (2w + 8)$ $196 = 4w + 16$ Now, subtract 16 from both sides: $180 = 4w$ Next, divide both sides by 4 to solve for $w$: $w = 45$

Thus, the width of the garden is 45 feet. The length is: $w + 8 = 45 + 8 = 53 \text{ feet}.$

Now, we can find the area $A$ of the garden, which is the product of its length and width: $A = \text{length} \times \text{width} = 53 \times 45 = 2385 \text{ square feet}.$

So, the area of the garden is $\boxed{2385}$ square feet.

Would you like more details on any step? Let me know if you have any further questions.

Here are some related questions you might find useful:

1. What is the perimeter of a rectangle if the length is twice the width?
2. How do you solve for the length and width of a rectangle if only the area is known?
3. What happens to the perimeter and area if the dimensions of the rectangle are doubled?
4. How can you express the dimensions of a rectangle in terms of a single variable given the perimeter?
5. How does the relationship between the length and width affect the area of a rectangle?

Tip: Always check that the perimeter equation correctly reflects the relationships in the problem. It's a useful step to ensure no errors in the problem setup.