Question

show how will you arrange three 6 Ohm resistors to get a total resistance of
i.4 ohms
ii.9 ohms

Answer 1

for 9 ohms , connect two in parallel and the third in series with the earlier combination of two resistors .
thus first two resistors in parallel,
        1/6 +1/6 = 1/r
       r = 3 ohms------ connect in series with third resistor
       R =3+6 ohms = 9 ohms
 for 4 ohms - two resistances in series and the third one in parallel with the combination of earlier two resistances.

Answer 2

If we arrange n resistors of value R ohms in series, the effective resistance:
     n R ohms
if we arrange n resistors of value R ohms in parallel, then the effective resistance:    R / n ohms

for getting effective resistance of 4 ohms from 6 ohm resistors, we can put two resistors in series, and their equivalent resistance = 12 ohms.  Then connect the third resistance of 6 ohms in parallel.
      equivalent resistance = 12 * 6 /(12+6) = 4 ohms.
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if we connect two resistors in parallel then effective resistance = 6/2 = 3 ohms.
We connect the third resistance in series.  The effective resistance: 3 + 6 = 9 ohms