Ḧ求助ᰦ这句英语句子成分怎么划分呀？

In the store, I asked each of my kids to pick something （that）they thought our “friend” there would appreciate.

to pick something 是不定式短语作宾补；

they thought our "friend" there would appreciate.是定语从句，修饰前面的something.

our "friend" there (那里的朋友)是从句的主语，would appreciate是从句的谓语，they thought 可以说是插入语。appreciate的宾语是先行词something,这里省略了that。

为您解答
一，
In the store,地点状语 I 主语asked 谓语each of my kids 宾语（to pick something they thought our “friend” there would appreciate.不定式做宾语补语）
二，
其中不定式的宾补里
to pick谓语 something宾语（省略了that，代something）/ they thought our “friend” there would appreciate定语从句/
三，
定语从句里
they从句主语 thought从句谓语（省略了that） /our “friend” there would appreciate宾语从句/
四，
宾语从句里
our friend从句主语 there定语 would appreciate从句谓语

该句话的主谓宾你分析对，to pick something 是不定式短语作宾语补足语。they thought ... appreciate 是定语从句，关系代词that由于作appreciate 的宾语，所以可以省去。