As you already have a topology for the circuit, you have several options. One option is to hand-analyse the circuit, into an expression in jω and the values of the components. This one has particularly simple form. Start from the parallel combination of L3 and R4 in parallel, let's call that Z3. Express the impedance of L3 as jωL3. Now Z3 is L3 in parallel with R4, Z3 = 1/(1/R4 + 1/jωL3). Now add R3 in series, and put that in parallel with L2, and continue up the ladder until you finally add R1, ending up with a power series in jω. It gets tedious, but it's possible. Now compare expression power term by power term with your input expression Z(f), where f=2πω. If you have exactly the same powers of jω in each, then match the coefficients. If they result in consistent and non-negative values for L and R, then you have yourself an exact synthesis. Unless it's an exam question that has been contrived to work exactly, it's more likely that you'll have spare power terms, or get impossible component values, in which case you're doing a best fit approximation. An alternative is optimisation, by either repeatedly analysing your circuit in Spice for instance, and tweaking values until the response matches Z(f), or by using optimising software which does that process quickly and automatically for you. I'd recommend doing hand optimisation with SPICE first, to explore the landscape of possible values. If you let automatic optimsation rip without understanding the regions of values in which solutions will be reasonable and so being able to constrain the optimser, then they tend to disappear off to infinity, or down local rabbit holes, without getting to solutions you're happy with.