It's a matter of emphasis, in this case you want to emphasize the action and not the result, eitherways, in this case you can choose either option subjectively depending on the message you want to convey.
I believe you can always use Genitive for objects of negated verbs. At least I can't think of a situation when it's impossible.
I also found this bit on Wikipedia:
Use of genitive for negation is obligatory in Slovene, Polish and Old Church Slavonic. The East Slavic languages (Russian, Ukrainian, and Belorussian) employ either the accusative or genitive for negation, albeit the genitive is more commonly used. In Czech, Slovak and Serbo-Croatian, negating with the genitive case is perceived as rather archaic and the accusative is preferred, but genitive negation in these languages is still not uncommon, especially in music and literature.
Both work, with a slight difference in meaning.
«Я этого не говорил» is imperfective, it represents not saying for some period of time (perhaps never). It works better for phrases you never intended to say.
The imperfective verb говорить represents action that has beginning and end. Negated, it represents not saying something for some period of time, a continuous not-saying.
«Я этого не сказал» is perfective: it means you didn't say something in a particular situation, at some paticular time. This works better for phrases you were planning to say, or should have said, but haven't. I.e. you had an opportunity to say something but you missed it, you didn't say something at some moment of time.
The perfective verb сказать represents a single, momentary action, that happens during a moment of time. Negated, it represents not saying something at some point of time, i.e. missing some chance to say something.
That's a bit off.
First, the verb in the exercise--говорил--is masculine past tense, and the approximate English transcription of the pronunciation would be gah-vah-REEL.
Second, the first person present tense would be говорю, which would be pronounced gah-vahr-YU.
Third, don't confuse the Russian letter в with the Latin letter b; they are not the same consonant. Russian в = Latin v, and Russian б = Latin b.
It depends. Sometimes you can change the word order without any difference. Other times it does make a difference, but it's too subtle to translate into English. And sometimes the difference is big enough to change the meaning of the sentence. And there are even cases when a certain word order is simply impossible and makes no sense (Russian word order is quite flexible, but it has its limits).
It's hard to answer your question without knowing what word order you've used.
Non-native student [so beware! :) ]:
My understanding is that order emphasizes the fact that you did not say THAT; you probably said something else instead, but not THAT.
The order "Я этого не говорил" emphasizes that you did not SAY that. Possibly you remained silent, instead of speaking.
Yeah, in this case the difference is pretty much negligible. As a native speaker, "я этого не говорил" sounds slightly more natural to me, but "я не говорил этого" is ok too. Also the former sounds a bit more assertive, but these tonal differences are really hard to explain. It's probably because the emphasis is on the verb.