let

x = the age of Tom

y = the age of Todd

Tom is 6 times as old as Todd:

x = 6y

In 6 years Tom's age will be 15 years more than 3 times as old as Todd:

x + 6 = 15 + 3(y + 6)

by solving the system of equations:

x = 6y

x + 6 = 15 + 3(y + 6)

we find:

x = 54 years

y = 9 years

click here to see the step by step solution of the system of equations:

Tom is 54 years old.