The cut you are after is from sB through BA through At.
The sB arrow comes from the left to the right. This direction determines the rest of the calculations. Count it as 2.
But the BA arrow comes from the right to the left. This is discarded, and counted as zero.
The At arrow comes from left to the right. It is counted as 2.
Thus the total, and the maximum flow, is 4. As you state, correctly.
I am still searching for an example where the minimum cut is not equal to (i.e. it is inevitably greater than) the maximum flow. The problem is that for complex examples, finding the minimum cut is not trivial. Theory says that there is always a minimum cut, and it is always equal to the maximum flow.