Finding the value of a specific resistor
The approach I would take to this problem is to work from left to right.


We know the total current so we can work out the voltage across the 8 ohm and 9 ohm resistors.
We subtract those voltages from the supply voltage to work out the voltage across the 60 ohm resistor.
We then work out the current in the 60 ohm resistor.
We subtract the current in the 60 ohm resistor from the total current to get the current that flows onward in the circuit.


Repeating this process we can work out all the voltages and currents in the circuit until we have the voltage and current at R. We can then attempt to calculate a resistance.

Note that only a limited range of current values are achievable. If the current specified is too high or too low the calculations will break down (and if you plow ahead anyway you will likely come out with a negative value for R).