At first:

Mandy had 182 muffins
Diana had 130 muffins

Mandy gave 4/7 to Diana = 182*4/7 = 104
So Now,
Mandy has 78
Diana has 234

Diana gave 1/9 to Mandy = 234/9 = 26
So Now,
Mandy has 104
Diana has 208
Hence,
Mandy = Diana /2
104 = 208/2

Mandy gave 78 more muffins than what Diana gave to Mandy

Mandy gave 104 to Diana &
Diana gave 26 to Mandy
Hence
104 = 26 + 78

Answer:
Mandy had 182 muffins
Diana had 130 muffins