She likes/favors he playing basketball.
或者 She likes/favors that he plays basketball. 后面that 引导谓语like/favor 的宾语从句,但这样看起来不够简洁,所以建议选择第一句,在like/favor 后面使用动名词(动词ing 形式作名词使用)。
She likes (that) he plays basketball.(这是宾语从句,从句部分即“他打篮球”要用陈述语序)
She likes watching him to play basketball.
She likes to look at him playing basketball.
She enjoys him playing basketball.