The pronoun their is the subject of the gerund. Here’s a more natural paraphrase: Their mechanic has recommended that they take their car to a foreign car expert.
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khoshtipI think you are referring to the first their of the sentence, yes?No the second one, before taking.
khoshtipThere are two ones. First one before taking and the second one after taking. Not?No.
AnonymousTheir mechanic has recommended them to take their car to a foreign car expert.I don’t find that very natural.
Anonymous Their mechanic has recommended them to take their car to a foreign car expert.No. it's not correct. For understanding the reason, please consider the word recommend. Their mechanic has recommended (what thing? to) them to take their car to a foreign expert.