Maths A-Level - Trigonometry - C3

I have been doing a past paper and got onto the question:

- Express 8 sin θ − 6 cos θ in the form Rsin(θ − α), where R > 0 and 0◦ < α < 90◦
I done this to get 10sin(θ-36.9)

Then the following question asks:
Find the greatest possible value of 32 sin x − 24 cos x − (16 sin y − 12 cos y)
as the angles x and y vary.
I rewrote this as 40sin(θ-36.9)-20sin(θ-36.9)

The answer is 60, but I just don't understand how to get this... I know max of sin graph is 1, and that there is a 40 and 20 in equation but why do you add them together? So confused, I can't visualise it.