What is the ruling on the money my maternal uncle is demanding from me, after my friend, whom I guaranteed, defaulted on his payment, knowing that my uncle lends money in exchange for it being returned multiplied?

What your maternal uncle is doing is precisely forbidden usury (riba), and Allah the Almighty has threatened those who engage in it with severe punishment. It is your duty to advise him and warn him against warring with Allah the Almighty. It is forbidden for you to assist him in this by bringing him someone who will borrow from him with usury, because this involves guiding to usury and assisting in it, based on the words of Allah the Almighty: (And do not cooperate in sin and aggression). Similarly, it is forbidden to guarantee a borrower who takes a usurious loan, because the guarantor might be compelled by the usurer to pay the usury along with the principal, and this is not permissible. Neither the guarantor nor the guaranteed is obligated to pay anything more than the principal, and it is not permissible for either of them to pay the interest.