。
She begged him not to interfere.
Literal
She [topic-は] him [to-に] not-interfere [in-order-to-ように-quotative-と] pleaded.
嘆願する ('plead, beg, entreat') is a strong, formal supplication verb — used for desperate requests, formal petitions, or earnest appeals. The doubled ように+と here is interesting: ようにと is sometimes used to combine the indirect-report ように with the quotative と — 'ように-quoted-as-the-content-of-pleading.' Some speakers and writers prefer this fuller form over plain ように for clarity. 邪魔する ('interfere, get in the way, intrude') is a everyday verb, here in negative form to express what was asked not to happen.