Learn Portuguese (Portugal): Ele exigiu que os filhos herdassem toda a fortuna. - He demanded that the children inherit the whole fortune.

The main verb exigiu (he demanded) is a verb of influence, which triggers the subjunctive because it imposes a will on someone else. Since exigiu is in the past tense, the sequence of tenses rule kicks in: a past-tense trigger requires the following verb to be in the imperfect subjunctive (herdassem) rather than the present subjunctive (herdem).

How do you form the imperfect subjunctive herdassem from the verb herdar?

To form the imperfect subjunctive, you always start with the third-person plural of the simple past tense (Pretérito Perfeito): herdaram (they inherited). You drop the -ram ending to get your stem (herda-), and then add the imperfect subjunctive ending. For os filhos (they), the ending is -ssem, giving us herdassem.

Could we just use the infinitive here and say Ele exigiu os filhos herdar...?

No, because the subjects of the two actions are different. Ele (he) is doing the demanding, but os filhos (the children) are the ones inheriting. When the subject changes after a verb of influence, you must use que followed by the conjugated subjunctive.

Why is there an a in toda a fortuna? Doesn't toda already mean "all"?