Jenny hopes that Mr Smith will suggest a good way to have her written English improved in a short

Jenny hopes that Mr Smith will suggest a good way to have her written English improved in a short period.
Jenny希望Smith先生会建议一个令她英文写作短期内提高的好办法.
主句很简单,是主谓宾结构：
Jenny(主) hopes(谓) that ...(宾语从句)
that引导的宾语从句又是主谓宾结构：
that Mr Smith(主) will suggest(谓,一般将来时) a good way(宾) to have ...(不定式作定语修饰a good way)
不定式：
to have (不定式非谓语动词) her written English(非谓语动词have的宾语) improved(过去分词非谓语动词作宾语补语补充说明her written English) in a short period(介词短语作improved的状语).
to have something done/improved/fixed/made/...是一个固定用法.再给你举几个例子：
I'm going to have my hair cut.
John had all his money stolen.
How many authors have had their lives made into movies?请问， 什么时候用过去分词做宾补 什么时候用现在分词 什么时候用不定式做宾补呢？这句宾语和宾补的关系是主表关系，即缺了系动词的主系表结构。所以加上系动词就是一个完整的句子：Her written English is improved.宾语用现在分词的宾补是主谓的现在进行时：Her written English is improving.这个意思和原句后面的时间状语(短时间内)不符。宾补用不定式的时候，宾语和宾补是主谓关系：He asked me to come. (I come)回到你的句子，have something done是固定用法，不能用不定式。