Bankers algorithm - How does it work?
To understand this problem you have to understand the rules for the safety checks. I am not going to give a detailed explanation of these but you can go here to read more about it. I will try to give an explanation of why C request 1 is safe but A request 1 is not.

There is a value associated with a process and a resource called need. The need is an n-tuple where n is the number of different resources. In this case n is just 1. Calculating the need is just taking the max and subtracting the has for each resource. And there is a safety check that if no process has a need less than or equal to the n-tuple of available  resources after a request then that request should be denied.

For C requests 1 it appears that the previous state is after B requests 1. In this C request 1 step we see A has a need (6), B has a need (1) and C has a need (4). Since there is only one resource the n-tuple of available resources is just (1) so this can be granted as B has a need of (1).

For A requests 1 the previous state is the initial state. We then calculate the need of A is (5), B is (2) and C is (5). And the resulting n-tuple of available resources is (1). There is no need which is less than or equal to this so we should reject it.

Be careful when reading more about the subject. The notation is often different, the letters A,B and C are often used to represent resources and p's will be used for processes. You will also be dealing with n-tuples of greater values.