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How to compute $213^{-1}$ modulo $466$?

Could you also provide me with an explanation of how to do it?

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    Relevant resources will be found at QA 241 (Library of Congress system) or 512.81 (Dewey decimal system). Or type "modular arithmetic" into Google.2012-05-21

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So you want to compute the inverse of $213$ modulo $466$? In other words you want to find $x$ such that $213x\equiv 1\text{ mod }466.$ More specifically you want to find $x$ and $y$ such that $213x+466y=1.$ Have you heard of the Euclidean algorithm?