A proportion says: (one fraction) is equal to (another fraction)
or (one ratio) is equal to (another ratio).
In this question, the ratio is (the area of a piece of carpet) to (the time it takes to manufacture it.
And we know we can write the ratio as (1 square yard) / (10 minutes).
The other ratio is (25.5 square yards) / (how long THOSE take).
The carpet factory works at a constant rate, so we know that those two ratios are equal. So we can write:
(1 yd²) / (10 min) = (25.5 yd²) / (how long that piece takes) .
To solve a proportion, you "cross multiply". That means
(left top) x (right bottom) = (left bottom) x (right top)
(1 yd²) x (how long the big piece takes) = (25.5 yd²) x (10 min)
There's an equation to solve.
Divide each side by (yd²):
(how long the big piece takes) = (25.5) x (10 min)
How long the big piece takes = 255 minutes
BUT ... the question wants to know "How many hours ..." , so you have to convert the 255 minutes into hours. You should be able to do that, because you certainly know that 60 minutes = 1 hour.
Big piece = (255 minutes) x (1 hour / 60 minutes)
Big piece = (255/60) hours
Big piece = 4.25 hours (that's 4 hours 15 minutes)