Since Bill needs to get at least one of each kind of donut, we can think of this problem as distributing 6 identical donuts among 4 different kinds of donuts with at least 1 donut of each kind.
This is equivalent to distributing 2 identical donuts among 4 different kinds of donuts with no restrictions.
Using stars and bars, we can find the number of ways to distribute the 2 donuts as $\binom{2+4-1}{4-1}=\binom{5}{3}=10$.
Therefore, there are $\boxed{10}$ different combinations that will satisfy Bill's order requirements.
The answer is: 10
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Bill is sent to a donut shop to purchase exactly six donuts. If the shop has four kinds of donuts and Bill is to get at least one of each kind, how many combinations will satisfy Bill's order requirements?

### Answer:
