This is a ratio problem; the ratio of the length to width is constant (and therefore equal):
4 /6 = 15 / x
Now, with a ratio, we may do any allowable algebra operation: cross-multiply, invert both sides, multiply or divide both sides by the same amount, etc.
Let's cross-multiply:
4x = (15)(6)
x = 90/4
x = 22.5 in.
It’s either Option 1 or 4

Above step we use "Multiplication property of equality"

In the above step we "Simplify on both sides of equation"

In the above step we use "Distribution property"

The above step is the result of using "Subtraction property of equality"

Above step is result of "Combining the like terms"

Above step is the result of using "Division property of equality"

Above step is result of "Simplifying fractions on either side of equation"
Proper fraction: 26 1/5
improper fraction: 131/5