Capacitors ran the combining rules backwards. Inductors put them back. Two coils in series add, and two coils in parallel take product over sum, exactly as resistors do. The job of this lesson is to keep the three components straight, and the only way to do that is to know WHY the coil sides with the resistor.

Fix the subscripts once: $L_1$ and $L_2$ are the inductances of the two coils as marked on their bodies, in henries, and $L_t$ is the single inductance the rest of the circuit actually sees, also in henries. Real parts are usually marked in millihenries (mH, a thousandth), and if both go in as mH the total comes out in mH. In series, $L_t = L_1 + L_2$, read aloud L-total equals L-one plus L-two. The same current threads both coils, each one builds its own opposing voltage when that current changes, and the two voltages stack. In parallel, $L_t = \dfrac{L_1 L_2}{L_1 + L_2}$, read aloud L-total equals L-one L-two over L-one plus L-two. A changing current now has two paths to split between, and two paths oppose a change less than either one alone.

So the sanity rails are the resistor's rails. Series lands above the larger of the two. Parallel lands below the smaller: below BOTH, not between them. Check every answer against those two sentences before you check the arithmetic. Both relations also run backwards when a design fixes the total and one coil is already fitted: $L_2 = L_t - L_1$ for a series string, and $L_1 = \dfrac{L_t L_2}{L_2 - L_t}$ for a parallel pair, where the fitted coil must be larger than the target or no partner can reach it.

One honest caveat: everything here assumes the coils are uncoupled, meaning neither one sits in the other's magnetic field. Wind two coils on one core and they share flux, and a mutual term joins the sum. That is the Electromagnetics chapter's business. On this bench the chokes are far apart, and the rules above are exact.