To determine the number of subsets of a set, you can use the formula:

$\text{Number of subsets} = 2^n$

Where $n$ is the number of elements in the set.

For the set $\{1, 2, 3, 4, 5, 6\}$, there are 6 elements. So, the number of subsets is:

$2^6 = 64$

Thus, the set $\{1, 2, 3, 4, 5, 6\}$ has 64 subsets.

Would you like to see how to list these subsets or any further details?

Here are 5 related questions to expand on this topic:

1. How many subsets contain exactly 3 elements from the set $\{1, 2, 3, 4, 5, 6\}$?
2. What is the number of proper subsets of $\{1, 2, 3, 4, 5, 6\}$?
3. How does the number of subsets change if the set has 7 elements instead of 6?
4. What is the formula for determining the number of subsets of a set with $n$ elements?
5. How can you calculate the number of subsets that include a specific element of the set?

Tip: The number of subsets always includes the empty set and the set itself.