To solve this problem, we need to work through each operation to reach the final result of 14.

1. Let the initial number be $x$.
2. The first operation subtracts 4, giving $x - 4$.
3. The second operation doubles the result, giving $2(x - 4)$.
4. The third operation adds 4, giving $2(x - 4) + 4$.

We set this final expression equal to 14 and solve for $x$:

$2(x - 4) + 4 = 14$

Expanding the terms:

$2x - 8 + 4 = 14$

Simplifying further:

$2x - 4 = 14$

Adding 4 to both sides:

$2x = 18$

Dividing by 2:

$x = 9$

So, the number that goes into the combobot is 9.

Would you like more details, or do you have any questions?

Here are some follow-up questions to deepen understanding:

1. What would the input be if the final output were 20 instead of 14?
2. How does each operation affect the result when starting from different initial values?
3. What if the "Double" operation were replaced with "Triple"? How would that change the solution?
4. Can we create an equation if we rearrange the order of operations?
5. How can we verify the answer by reversing the operations?

Tip: When solving multi-step problems, break down each operation step-by-step and write an equation to represent the sequence.