Was the difference between "hallok" and "hallom" introduced here? Please, help to understand.
Hallok is indefinite, hallom is definite. Here's a conjugation table: http://www.hungarianreference.com/Verbs/Conjugation/
Definite conjugation is used when the verb has a definite (direct) object. (Although you really shouldn't call objects direct objects, not when talking about Hungarian.) Direct objects roughly correspond to nouns with definite articles. You can find the complete list at the wiki page about Hungarian verbs.
So: Hallom a fiúkat. = I hear the boys.
Hallok fiúkat. = I hear boys.
Objects are often implicit, & since first & second person pronouns are indefinte, while third person pronouns are definite, those can be often left out too. (& there's also a completely different conjugation for first person singular when the object is second person.)
Hallasz. = You hear. (as in you're not deaf) OR more often You hear me.
Hallod. = You hear it.
Hallok. = I hear.
Hallom. = I hear it.
Hallak. = I hear you.
I think it is incorrect. To translate 'a' [definite article] in this context, you need to use the specific determiner 'the' [definite article].