In this question there are numerous important information's that can be used to deduce the required answer. Firstly it is already given in the problem that the ratio at which the stamps have been shared between Alice, Bernice and Cheryl is 8:9:18. Also it is given that Alice received 184 stamps from the total number of stamps and that too as per the ration in which the stamps have been divided. Now we have to find the common ration to actually deduce the number of stamps received by Bernice and Cheryl.
Let us assume the common multiple to be = x
Then we can use the case of Alice to find the common multiple.
8x = 184
x = 184/8
= 23
Then
The number of stamps received by Bernice = 9 * 23
= 207
The number of stamps received by Cheryl = 18 * 23
= 414
S Bernice received 207 stamps and Cheryl received 414 stamps