Jean is 16.

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.)

 

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