This sentence was said by Arthur in the TV show Arthur. He was teased when he wore glasses to school, and now he threw them away and said:
I won't even know where they land.
I'm not sure what he meant when he said "won't even know".
Arthur can't see without his glasses, so he says he won't know where they land because he will not just dispose of them but literally throw them, and as they fly through the air, he will no longer have sight of them. Therefore, he won't be able to see where they land. It's a play on the phrase "throw away" to mean both dispose and to toss through the air.
"even" here is an intensifier, often used to stress something surprising, as in:
"Even my grandmother plays World of Warcraft".
"won't" is used simply as the negative of "will" - I am throwing my glasses away but I will not know where they land.
Presumably he is saying that he is not planning to look where his glasses land so he can get them later.