The right way to read a circuit
I find it helpful to work right to left. The last gate is an OR gate. Forget about what the actual inputs are for the moment. They're just two inputs. Let's call them X and Y.







simulate this circuit &ndash; Schematic created using CircuitLab

Now let's look at the X input. You already appear to understand that it is (A AND B), so let's substitute that in for X:  







simulate this circuit

Obviously, input Y is nothing more than (NOT B), so substitute that in for Y:  







simulate this circuit

And that's it.