Let R be the remaining cupcakes after she gave 84 of them to her neighbour.

Number of cupcakes aunt received = 2/5*R of total cupcakes

= 2/5R of total cupcakes

Number of cupcakes that are left

= 3/5*R of total cupcakes

=3/5R of total cupcakes

Since she is left with 1/4 of the total number of cupcakes, 

3/5R = 1/4

R      =  5/12

Number of cupcakes that neighbour received

= 7/12 of total cupcakes

Since 7/12 of total cupcakes = 84 then, 1/12 of total cupcakes = 12

Number of cupcakes aunt received

= 2/5*R of total cupcake

=2/5*5/12 of total cupcake

=2/12 of total cupcake

=24 cupcakes

Aunt received 24 cupcakes