Two resistors with values of 6.0 w and 12 w are connected in parallel. this combination is connected in series with a 2.0 w resistor and a 24 v battery. what is the current in the 2.0 w resistor?

6.0 Ω  is the correct answer

Here, Equivalent resistance of two resistors in parallel:

1/R = 1/R1 + 1/R2
1/R = 1/6 + 1/12
1/R = 2+1/12
1/R = 3/12
R = 12/3
R = 4 Ohm

Now, Equivalent resistance of the circuit = R = R1 + R2
R = 2 + 4 = 6 Ohm

Now, we know, R = V / I
2 = 24 / I
I = 24/2
I = 12 A

In short, Your Answer would be: 12 Ampere

Hope this helps!