He knows better than _____(do) such a silly thing.

to do

know better than+ to do 有头脑，懂道理；不至于蠢到…，不会上当

does

to do

know better than to ...

填to do
这是固定句型，know better than to do/ that 是明事理而不至于做某事的意思。
句子意思是：他明白事理不会做这样的蠢事的。

better than doing.

固定短语，better than doing. 不应该会的意思。