Required Probability=$\frac{No. of Favourable Ways }{Total no. of Ways}$
No. of favourable ways= ^{2n}C_{n } (bcoz select exactly n heads out of 2n tosses )
Total no. of ways= 2n tosses and each have 2 possibilities either H or T so total=$2^{2n}$=$4^n$ possibilities
So Ans is $\frac{\binom{2n}{n} }{4^{n}}$ which fits option A.