question about "they" , and "each"
In 2000, the price of oil started at just under $30, and the food price index begun at under 100 points. Both prices stood at around the marks where they begun for the following four years.

My question ; Either 'where they begun' or 'where each begun' can be used in this sentence?

Question

question about "they" , and "each"
In 2000, the price of oil started at just under $30, and the food price index begun at under 100 points. Both prices stood at around the marks where they begun for the following four years.

My question ; Either 'where they begun' or 'where each begun' can be used in this sentence?

Answer

Irregular verbs in English (to begin):
Where they "had" begun - begun is the past participle of the verb "to begin" and requires the verb "to have" as a helper.
Where they began - began is the simple past tense of the verb "to begin" and requires no helper verb.

So in answer to your question, these can all be used in the sentence:
Where they began OR Where they had begun, Where each began OR Where each had begun

Answer

The sentence has many mistakes - is it by a native speaker??   Where is it from?
eg:  began, not begun   /  around the mark, not marks   /  the following, not 'for'