Solving the circuit by hand is very simple (considering all components as ideal), since the gain of the proposed configuration is G=-Zfeedback/Zseries then:
|G| = -abs[ (R2 + jwL2)/(R1 + jwL1) ]
From this we can see that G(0) = -R2/R1 and G(infinite) tend to -L2/L1. Using the values of the assignement R2/R1 = 100 and L2/L1 =2
L2/L1 = 2 is not met in the proposed schematic that shows instead 0.5 (could by a typo).
In order to calculate all the value we can use the -3dB frequency f = 1/(2*pi*L/R) so that if we set arbitrary R1 to 100 ohm then:
R2 = 10k
L1 = 100/(2*pi*20) = 0.796 H
L2 = 1.59 H
That are the same values found by FvM. At these two frequencies (20Hz and 1k) we will not have the required values but at 20 Hz we will have -100/sqrt(2) = -70.7, while at 10k we will have -2*sqrt(2) = -2.8. Furthermore we have not enough degrees of freedom to fix both lower and higher frequency amplitudes. I've checked before the pairs (20Hz,-100) and (1k, -2) are consistent.