(b) That's right. The facts certainly establish that there is an agreement between A and B. But we also know that not all agreements are intended to be legally binding.
The very few facts given in this example do not really provide a sufficient basis on which to infer (draw a proper conclusion from the facts that are known) that A and B intended to be legally bound by their agreement. To draw an inference about A and B's intention It would help to know more. For example, B might be a person who operates a commercial gardening service, in which case a legally binding contract is more likely to be intended. Or B might be A's child, keen to earn some pocket money, in which case such an intention to be legally bound is less likely.
The first thing to find out, therefore, is what sort of additional facts might make it easier to infer when the parties to an agreement intend to be legally bound. For example, in Carlill v Carbolic Smoke Ball Co [1893] 1 QB 256, the seriousness of the Smoke Ball Company's intention to be bound was evidenced by a deposit of money into a bank account for the purpose of paying a promised reward.