DC circuit theory: Equivalent resistance help
You're right.

Two things to know :

Series : Rs = R1 + R2

Parallel : Rp = R1*R2 / (R1 + R2) or 1/Rp = 1/R1 + 1/R2

Here, you've got

R1 = 100;
R3 = 200;
R4 = 400;

Re = 100;

Ra = R1*R3/(R1 + R3) (considering Ra is the upper branch equivalent resistor)
Rb = Re - Ra (which is equal to R2//R4 = R2*R4/(R2 + R4))


You find Rb is 33.333 Ohm. Now you can compute : 

1/Rb = 1/R2 + 1/R4 
1/33.333 = 1/R2 + 1/400
1/R2 = 1/33.333 - 1/400 = 0.0275
R2 = 1/0.0275 = 36.3636


Then you can check the answer by R1//R3 + R2//R4 = Re.