A function is self dual if it is equal to its dual (A dual function is obtained by interchanging $.$ and $+$).
For selfdual functions,
 Number of min terms equals number of max terms
 Function should not contain two complementary minterms  whose sum equals $2^{n}1$, where $n$ is the number of variables.

A 
B 
C 
0 
0 
0 
0 
1 
0 
0 
1 
2 
0 
1 
0 
3 
0 
1 
1 
4 
1 
0 
0 
5 
1 
0 
1 
6 
1 
1 
0 
7 
1 
1 
1 
so here
$(0,7) (1,6) (2,5) (3,4)$ are complementary terms so in selfdual we can select any one of them but not both.
totally $2\times 2\times 2\times 2 =2^4$^{ }possibility because say from $(0,7)$ we can pick anyone in minterm but not both.
For example, let $f = \sum (0,6,2,3)$
NOTE:here i have taken only one of the complementary term for min term from the sets.
so remaining numbers will go to MAXTERMS
For above example, $2^4 =16$ self dual functions are possible
So if we have $N$ variables, total Minterms possible is $2^n$
then half of them we selected so $2^{n1}$.
and now we have 2 choices for every pair for being selected.
so total such choices $=\underbrace{2\times 2\times 2\times 2\dots 2}_{2^{n1}\text{ times} }$
∴ $2^{2^{n−1}}$ (option D)