Let the year Jeff will be twice as old as his brother be x
In x years, their ages are:
Jeff: 10 + x
Jeff's brother: 2 + x
In x years, Jeff's age will be twice as his brother's age:
10 + x = 2(2+x)
10 + x = 4 + 2x
2x-x = 10 - 4
x = 6 years
Their ages in 6 years:
Jeff: 10 + x = 10 + 6 = 16 years old
Jeff's brother: 2 + x = 2 + 6 = 8 years old