Mr. charles cut fresh roses from his garden and gave 10 roses to his neighbor. then he gave half of what was left to his niece. he kept the remaining 14 roses. how many roses did he cut?

Mr. Charles had cut 34 roses

Here's why:
He gave 10 roses to his neighbor
He has 14 cut roses left
10 + x = y
He originally gave half of what was left before having 14 roses
So retracing his steps 14 x 2 = 24
x = 24
10 + 24 = 34
y = 34 roses