A rectangular garden has a width that is 6 feet shorter than its length. The area of the garden is 180 square feet. If the garden is to be extended with a pathway that is 2 feet wide around the entire garden, what will be the total area of the garden including the pathway?

To find the dimensions of the garden, let the length be denoted by $L$ and the width by $W$. Based on the problem, we can express the width in terms of the length:

$$ W = L - 6 $$

Substituting this relationship into the area equation:

$$ L \cdot W = 180 $$

So, we have:

$$ L \cdot (L - 6) = 180 $$