How can this current division happen?
I don't follow the reasoning in the given solution, but I recommend that instead of memorizing a &quot;current divider formula&quot; in terms of resistors, you remember it in terms of conductors.



simulate this circuit &ndash; Schematic created using CircuitLab
$$I_2 = I_s\frac{G_2}{G_1+G_2}$$
or
$$I_2 = I_s\frac{1/R_2}{1/R_1 + 1/R_2}$$
Then it's easy to see, since your current divider involves a 3 kohm resistor, and a series combination of 2 and 4 kohms, and you want the current through the series combination, the current will be
$$i = i_s\frac{1/6}{1/3+1/6} = i_s\frac{1}{2+1}$$
which gives the same result as in the presented answer (2 mA).