Given that Joseph went to buy at least one of each of cake, cookie & donut costing $5, $6 & $10 respectively and he needs to spend any amount between $30 & $36, both inclusive. And we need to find in how many ways he can purchase the items

Given that he has to buy at least one of each
=> Total amount spent on buying one cake, one cookie and one donut = $5 + $6 + $10 = $21
He has spend between $30 and $36 inclusive
=> Money left to be spent is in between $30 - $21 and $36 - $21 inclusive = $9 and $15 inclusive

Following are the cases possible
Only cake cases
1 cake (not possible) as it will be on $5 and we need to spend between $9 and $15 inclusive
(1) 2 cakes => Money spent = 2 * $5 = $10
(2) 3 cakes => Money spent = $15

only cookie cases
1 cookie (not possible) as it will be on $6 and we need to spend between $9 and $15 inclusive
(3) 2 cookies => Money spent = 2 * $6 = $12
3 cookies (not possible) as it will be on $18 and we need to spend between $9 and $15 inclusive

only donut cases
(4) 1 donut => Money spent = $10
2 donuts (not possible) as it will be on $20 and we need to spend between $9 and $15 inclusive

Cake + Cookie
(5) 1 cake + 1 cookie = $5 + $6 = $11
Other cases not possible as sum will cross $15

Cake + Donut
(6) 1 cake + 1 donut = $5 + $10 = $15
Other cases not possible as sum will cross $15

Cookie + Donut
Not possible as 1 cookie + 1 donut will cost $6 + $10 = $16

=> Totally 6 choices.

So, Answer will be E
Hope it helps!