To find out how many eggs are left, we first determine the total number of eggs the Coleman family bought.
The family bought 6 crates, and each crate contains 12 eggs. Therefore, the total number of eggs can be calculated as follows:
\[ \text{Total eggs} = \text{Number of crates} \times \text{Eggs per crate} = 6 \times 12 = 72 \]
Next, we need to account for the eggs that have been eaten. They have eaten 16 eggs, so we subtract that number from the total:
\[ \text{Eggs left} = \text{Total eggs} - \text{Eggs eaten} = 72 - 16 = 56 \]
Thus, the number of eggs left is:
\[ \boxed{56} \]