This problem requires----- with great care.

This problem requires studying with great care。
解析：
1。被动式：当一个动名词逻辑上的主语所表示的是这动作的对象时,动名词一般要用被动形式。
His being neglected by the host added to his uneasiness。
He couldn’t bear being made fun of like that。
2。但要注意,在want,need,deserve,require 等动词后,尽管表示的是被动的意思,却用动名词的主动形式。
My pen needs filling。
The point deserves mentioning。
This problem requires studying with great care。
在worth这个形容词后情形也是这样。
Her method is worth trying。
希望能够帮到您!