To keep our notations simple, we denote the gifts by the initials of the children. The space of all possible outcomes, the sample space, can be represented as a set of ordered triplets $\Omega=\{(A,B,C),(A,C,B),(B,C,A),(B,A,C),(C,A,B),(C,B,A)\}$.

Since there are 6 outcomes, the size of the powerset is $2^6 = 64$.

Additional Notes:

The power set is the set of all possible subsets of the sample space. To give you a few examples, the following subsets are parts of the powerset:

$\{(A,B,C),(A,C,B)\}$

$\{(B,C,A),(B,A,C),(C,A,B),(C,B,A)\}$

$\{(A,B,C),(A,C,B),(B,C,A),(B,A,C),(C,A,B),(C,B,A)\}$

$\emptyset$

To understand the formula for the powerset, think about constructing a subset of outcomes. For each outcome, you have to decide whether to put it into the subset or leave it out. That's 6 different decisions, each one with two outcomes, so the total number of paths you can take is $2^6$.