Answer
The $16$ subsets are:
$\{\}, \{a\},\{b\},\{c\},\{d\}, \{a,b\},\{a,c\},\{a,d\},\\
\{b,c\},\{b,d\},\{c,d\}, \{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\}, \text{ and }\{a,b,c,d\}$.
Work Step by Step
The subsets with no elements are: $\{\}$.
The subsets with $1$ element are: $\{a\},\{b\},\{c\},\{d\},$.
The subsets with $2$ elements are: $\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\}$.
The subsets with $3$ elements are: $\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\}$.
The subsets with $4$ elements are: $\{a,b,c,d\}$.
Thus there are $16$ subsets.
