resistance of 4 ohm, 10 ohm and 7 ohm is connected in parallel.
so net resistance in parallel is given by
[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}[/tex]
[tex]\frac{1}{R} = \frac{1}{4} + \frac{1}{10} + \frac{1}{7}[/tex]
[tex]R = \frac{140}{69} ohm[/tex]
now it is connected to 6 ohm resistance in series
so net resistance is given by
[tex]R_{net} = R_1 + R_2[/tex]
[tex]R_{net} = 6 ohm + \frac{140}{69} ohm[/tex]
[tex]R_{net} = 8.03 ohm[/tex]