When I want to measure Inductance Through LCR
how do I know when use series & parallel mode
When I need to use in series
When I need to use in parallel
The choice between measuring inductance in series or parallel mode depends on the type of circuit you are measuring and the characteristics of the inductor.
In series mode, the inductor is connected with a known impedance (usually a resistor), and the LCR meter measures the circuit's total impedance. This is useful when measuring the inductance of a coil in a circuit with a relatively low DC resistance. You want to measure the inductance without interference from the DC resistance.
In parallel mode, the inductor is connected with a known capacitance (or sometimes resistance), and the LCR meter measures the circuit's reactance. This is useful when measuring the inductance of a coil in a circuit with a relatively high DC resistance. You want to measure the inductance without interference from the DC resistance.
There are many scientific articles on the subject; one example is "Measurement of Inductance" by David A. Johnson, IEEE Transactions on Instrumentation and Measurement, Vol. IM-30, No. 3, June 1981, which you can find in IEEE Xplore Digital Library, it gives a detailed explanation of the theory and methods of measuring inductance.
Never had heard that two knobs may be connected in parallel or serial. Just connect and forget it. Parallel or non-parallel have meaning when one is measuring MULTIPLE inductances by one shoot. Or, in some extremely rare measurers, just aiming to spining the head, the R value may be shown as ESR or contrary EPR. Then who is stopping You to recalc one to each another? Its rather simple math of form 12 autumn session in secondary school.