An initial remark: when working with percents, it can be good to remember that the percent sign is simply another way of denoting hundredths. 40% and 40/100 are identical values; they just have different representations.
With that in mind, having knowledge of what taking 10% of something means is an excellent stepping stone when dealing with taking some multiple of 10%, like the 40% in this problem. When we take 10% of something, that's the same thing as saying we're taking 10/100 of it, which is again the same thing as saying we're taking 1/10 of it, or dividing it by 10. Let's use that fact as a jumping-off point for this problem.
10% of 920 cups is 920/10, or 92 cups. Since 40% = 10% x 4, all we need to do to obtain our answer is multiply that 92 by 4, obtaining an answer of 92 x 4 = 368 cups.