簡單句子理解問題

只有 smoking has 是用作補充 the effect。
"smoking has" is a relative clause to qualify the effect. "on him" is not part of the relative clause but follows directly after "the effect".

Without the relative clause, the sentence reads:
He does not seem to care about the effect on him.
It does not tell what kind of effect it is.

He does not seem to care about the effect (that/which) smoking has on him.
With the relative clause, we know it is about the effect of smoking. You can also write it this way:
He does not seem to care about the effect of smoking on him.

我不了解所引用英語句法 ?
唯本二十三國產普通港話 =
Zi You Xuan Wen Ti Suo Ren Qu Pian Ou Na Mei Li Ke Ju He Guo Fa Er Ding Chi Ben An 23

Look no further. Garlic2010's answer is correct and concise.

Rewritten with no verb"has"
The Predicate:-smoking effect-------indirect object
---------------------------on him--------------direct object
The sentence:-
He does not seem----------------------Subject +verb
to care----------------------------------------infinitive
about the smoking effect--------------indirect object
on him-----------------------------------------direct object
(the smoking effect),whether predicative or complementary,are invariably for the subject to refer to.

2012-07-30 13:43:14 補充：
The Q lacking word"what",&should be dropping "smoking has",but adding "effect".