Let x be the Expected Number of tosses.
If we get a tail immediately (Probability $\frac{1}{2}$ ) then the Expected number = (x+1)
If we get a head then a tail (Probability $\frac{1}{4}$ ) then the Expected number = (x+2)
If first 2 tosses are head then the Expected number =2
Thus
x = $\frac{1}{2}$ (x+1) + $\frac{1}{4}$ (x+2) + $\frac{1}{4}$ 2
$\frac{1}{4}$ x = $\frac{3}{2}$ x
x=6
Hence (c) 6 is the Answer.