This is, in fact, a middle or high school-level problem. Forum rules ask thread starters to show some effort. In this case this may mean writing equations describing the relationship between the quantities of counters in the three boxes or describing what you do and don't understand about this problem.
Let a be the number of counters in box A, b the number of counters in box B, and c the number of counters in box C.
"The ratio of counters in box A to box B is 5:3."
so a/5= b/3 and 3a= 5b
"The ratio of counters in box B to box C is 2:1."
so b/2= c/1 and b= 2c.
"Some counters are removed from box A."
Call the number of counters removed x. Now there are a- x counters in box A.
"54 counters are moved from box B to box C."
Now there are b- 54 counters in box B and c+ 54 counters in box C.
"There are now the same number of counters in each box."
a- x= b- 54 and b- 54= c+ 54.
We have four equations
a- x= b- 54 and
b- 54= c+ 54
to solve for a, b, c, and x.