(b) That's right. In this example, A's promise is not contained in a deed: it is an informal agreement. And in Australian law, not all informal agreements are enforceable. An informal agreement is legally binding only if, at the time the agreement is made, each party gives something in exchange for what they are getting.
Whatever is given by each party, at the time the agreement is made, in exchange for what they are getting is called 'consideration'. In this example, B has not given anything at all to A in exchange for A's promise. We can explain why there is no legally enforceable agreement simply by saying: B gave no consideration for A's promise.'