equivalent resistance
Suppose you have a tangle of resistors inside a box, with just two wires poking out. The equivalent resistance is the single resistor you could swap the whole box for, such that anything connected to those two wires could never tell the difference. It is the answer to a very practical question: from out here, how hard is it to push current into this thing?
For networks built only from series and parallel pieces, you find it by reducing the circuit inward, one step at a time. Spot a group of resistors clearly in series and add them; spot a group clearly in parallel and combine them with the parallel rule; replace each group with its single equivalent, then look again for new series or parallel groups, and repeat until one number remains. For instance, a 100 ohm in series with the parallel pair of 200 ohm and 200 ohm becomes 100 + 100 = 200 ohm.
This reduce-and-conquer skill is the workhorse of hand analysis: once a complicated network collapses to one resistor, Ohm's law gives you the total current in a line. But be honest about its limit. Not every network is purely series and parallel. A balanced or unbalanced bridge, for example, has resistors that are neither cleanly in series nor cleanly in parallel, and then you must reach for nodal analysis, mesh analysis, or a delta-to-wye transform instead.
Reduce a 300 ohm in series with (600 ohm parallel 600 ohm). The parallel pair is 300 ohm, so the equivalent is 300 + 300 = 600 ohm. A 12 V source across the terminals then draws 12/600 = 20 mA.
Collapse series and parallel groups inward until one resistor remains, then apply Ohm's law.
Series-parallel reduction does not solve every circuit. Bridges and other non-ladder topologies need nodal or mesh analysis, or a delta-wye transform.