So for me to solve your question, I will follow exactly what is in the text but I will alter the diagram a bit to get to a diagram that might solve the problem.
The L and W at the top of the pattern need to be re-drawn to scale so that they will match the L and W that are at the left and right sides of the pattern.
When that is done, then,
2L = 3W
L = 1.5W
Thus, the pattern is (W +W +W) high by (W +L) wide.
That is, the pattern is 3W high by 2.5W wide.
So if the area to be covered is 12L long by 10L wide, then, in terms of W, that is
(12*1.5)W long by (10*1.5)W wide
18W long by 15W wide.
If there is no preferred way to lay out the pattern, other than the way to minimize cuttting, then we lay them out such that the width of the pattern is along the width of the area to be covered.
Becauce, along the width of the area, 15W / 2.5W = 6 patterns
And along the length of the area, 18W / 3W = 6 patterns too.
So the are 6*6 = 36 patterns all in all to cover the area exactly.
In one pattern there are 5 rectangles that are L by W.
Therefore, 36*5 = 180 rectangles are needed. ----------answer.