。
She thoroughly drilled the basics of English grammar into her students.
Literal
She [topic-は] students [recipient-に] English-grammar [possessive-の] basics [object-を] sufficiently teach-drove.
十分に ('sufficiently, fully') is built from 十分 ('enough, adequate') + に for adverbial use — the same na-adjective + に pattern that underlies most Japanese manner-adverbs. Layered with 教え込む (a compound: 教える 'teach' + 込む 'drive in fully'), the sentence paints thorough pedagogy: the basics weren't just covered, they were drilled until they stuck. 教え込む belongs to the productive 込む family of compounds (押し込む 'push in,' 信じ込む 'believe firmly,' 巻き込む 'drag into') that all share the 'do completely / drive inward' flavor. The に on 学生に marks the recipient of the teaching.