(a) To get 4 Ω equivalent resistance, 3 Ω and 6 Ω resistors are connected in parallel and 2 Ω in series.

When 3 Ω and 6 Ω are added in parallel.

1/R_P = 1/R₁ + 1/R₂

1/R_P = 1/3 + 1/6

1/R_P = (2+1)/6

1/R_P = 3/6

        = 2Ω

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When its equivalent resistance is connected in series with a resistor of 2 Ω, then

R_S = R₁ + R₂

R_S = 2 + 2

    = 4Ω

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When all three resistors are connected, the equivalent resistance is 1 Ω.

1/R_P = 1/R₁ + 1/R₂ + 1/R₃

1/R_P = (3 +2 + 1)/6

1/R_P = 6/6

      = 1/1

R_P   = 1Ω