The length of a rectangular garden is 3 yards more than its width. The perimeter of the garden is 38 yards. Find the width of the garden.

Let $W$ be the width of the rectangular garden.
Let $L$ be the length of the rectangular garden.
From the problem, the length is 3 yards more than its width:

$$L = W + 3$$

The perimeter of the garden is 38 yards:

$$P = 38$$

The perimeter $P$ of a rectangle with length $L$ and width $W$ is given by:

$$P = 2(L + W)$$

Substitute $L = W + 3$ and $P = 38$ into the formula:

$$38 = 2((W + 3) + W)$$

First, combine the terms inside the parentheses:

$$38 = 2(2W + 3)$$

Divide both sides by 2:

$$\frac{38}{2} = 2W + 3$$ $$19 = 2W + 3$$

Subtract 3 from both sides:

$$19 - 3 = 2W$$ $$16 = 2W$$

Divide both sides by 2:

$$W = \frac{16}{2}$$ $$W = 8$$

The width of the garden is $\text{8 yards}$.