Translation:The teacher gave us a lot of homework.
You can use "dar".... but when you give something to someone, you can also use that (you will passar (give) something) "me passa seu número?" - you use that for asking one's phone number. "Me passa o garfo?" (The fork is near the person you're talking to, and then you ask him to "pass" it for you) "o quê você vai passar de tarefa?" (What will you "pass" (give) as a homework?)
Homework also means "tarefa". it is the most common way to say that. "Dever de casa" is also correct, but not so frequently used. "Bastante" means a lot of, too much/many. it means "enough" when I use "o bastante". "Eu comi bastante" = I ate a lot; "Não comi o bastante" = "I haven't eaten enough". In negative sentences, use just "bastante" to mean enough: "Minha casa tem bastantes janelas" - "My house has many windows" / "Minha casa não tem bastantes janelas" - "My house does not have enough windows"
But many people do not use "bastantes", once it means something abbundant. But the correct is to use that in plural.
As adverb, it works as "very"/"a lot" - "Ela está bastante (muito) cansada" = "She's very tired" / "Ela fala bastante" = "She talks a lot"
If you have any doubt, change bastante for "muito", which works the same way (singular/plural). Hope that helps
well, if I should use "o bastante" in negative sentences, how to translate then "enough" in affirmative sentences e.g. "I like moderation in eating: not too little nor too much, just enough" , "We've talked enough, it is time to work!" or "I've had enough of your lies, I don't believe you anymore".
The way I use it, "bastante" means "a lot" and "O bastante" means "enough"
Dever de casa and Lição de casa are the most common ways to refer to Homework (at least in Rio and São Paulo). I had never heard "tarefa" (which means "task" ) being used as homework. What region is that from? :)