το μεν προτερον βουλευμα ουτως γιγνεται, το δ’υστερον ωδε το πληθος τω Δεμοσθενει επειθετο.
The answer key gives: "The previous resolution comes (or came)about in the aforementioned way, the later resolution in the following way: the multitude obeyed Demosthenes.
A) ουτως γιγνεται - makes no sense: ουτω needs the sigma when followed by a vowel, which is not the case here,
B) the key translates ουτω and ωδε as if coming from the demonstratives “ουτος” and “οδε” (“aforementioned” and “following”) instead of from the adverbs.
As to A: οὕτως is used without the sigma before a consonant by several authors including Aristophanes and Plato, so it’s one of those rules tends to “get broken”. Have a look at the entry for οὕτως in the LSJ. I know you shouldn’t have to resort to the LSJ for a textbook exercise, but that is where I found the answer.