circuit in neither series or parallel (is wye delta transformation necessary?)
Most of these sorts of problems are drawn in a way to confuse the student.

I would re-draw your circuit like so:







simulate this circuit &ndash; Schematic created using CircuitLab

R 5, 6, and 7 are in parallel, and all 12 Ohms, so the equivalent resistance of that group is 4 Ohms.

R5,6,7 plus R3 is 14 Ohms, which is in series with the unknown R4, so the circuit simplifies to







simulate this circuit

Since we want an equivlaent resistance for the whole circuit of 50 Ohms, R2 (60 Ohms) in parallel with R3 (14 Ohms) and R4 (unknown) in series must equal 20 Ohms

The remainder of the solution is, as they say, left as an exercise for the student.