Question

grandpa's age is 6 years less than 6 times juniors age. their sum of their age is 78.

Answer 1

6n-6 = Grandpa
n = junior

6n-6+n = 78
   +6        +6
7n = 84
/7      /7
n = 12

6(12)-6 = Grandpa
72-6= 66

Junior  is 12 years old, Grandpa's age is 66 years old

Answer 2

Grandpa is 66, Junior is 12. 
Grandpa= 6x Juniors age - 6
Grandpa + Junior = 78
78-J = 6J - 6
78 + 6 = 6J + J
84 divided by 7 and  7J divided by 7. 
J = 12, so grandpa must be 66.