$AB+\bar{A}C+BC+\bar{A}C$ can be written as
$$AB + \bar{A}C + BC$$
because $\bar{A}C$ was written twice
Now, finding the DUAL of above expression gives
$$(A+B)\cdot(\bar{A}+C)\cdot(B+C)$$
Applying consensus theorem we get
$$(A+B)\cdot(\bar{A}+C)$$
hence option (a) is correct