Sure, let's solve this step by step.
To find the missing digit we need to know that:
1. If a number is divisible by 3, the sum of all of its digits is divisible by 3.
2. If a number is divisible by 4, its last two digits form a number that is also divisible by 4.
Firstly, find the sum of the given digits in the number, which are [7, 3, 4, 6, 2, 8, 5, 5, 6]. The sum of these digits is 46.
Next, we want to find the digit that, when added to this sum of 46, results in a number that is divisible by 3. Start by checking with the digit 0, if adding 0 to the sum yields a number divisible by 3. If not, increment the digit and check again. Continue doing this until we find a digit that makes the sum divisible by 3.
In this case, the digit we are looking for is 5 because when you add 5 to 46 you get 51, which is divisible by 3.
Now, we also need to ensure the last two digits (the missing digit and 6) when put together form a number that is divisible by 4.
The number '56' made by our missing digit 5 and the given digit 6 after the underscore is divisible by 4.
Hence, the missing digit is 5.