Let x represent Joan's age. Let y represent Jane's age. Let z represent Jean's age.

Jean is Joan's daughter and she is 12 years younger than her aunt.

So z = y - 12.

Joan is twice as old as Jean.

So x = 2z.

Four years ago, Joan was the same age as Jane is now, and Jane was twice as old as her niece.

So x - 4 = y and y - 4 = 2(z - 4).

If we solve the last equation for y we can substitute that value of y into the first equation to solve for z.

y - 4 = 2(z - 4)

y - 4 = 2z - 8

y = 2z - 4

Now substitute this value for y into the first equation.

z = y - 12

z = 2z - 4 - 12

z = 2z -16

z = 16

We didn't use any information about Joan's age to solve the problem, so let solve all the ages to make sure we have the right answer.

z = 16 Jean (12 years younger than Jane.)

x = 2z so x = 32 Joan (Twice as old as Jean and four years ago same age as Jane is now.)

x - 4 = y so y = 28 Jane (Four years ago she was twice the age of Jean.)