At first it seemed like 教给 is just a verb and a preposition, but 教 can be used directly: 我可以教你。 Is that a separate piece of vocabulary?
2 Answers
We use "教" as "teach", e.g., "我可以教你" = "I can teach you", "他教数学" = "He teaches math", "(这道题)我教过你了" = "I have taught you (how to solve) this question."
When we say "教给" we usually mean "give", like "这件事/物品交给你了" = "This thing is given to you,(and from now on you should be responsible for it)", "把这本书教给Tom" = "Give/Bring this book to Tom". However, sometimes we can use "教给" as "teach", depending on "what" you give to someone. For example, "你来教他这个技术" = "(你)把这个技术/方法教给他" = "(You) teach him the technique/way (of doing ...)"
In fact,教(jiao)it could combine with anyone or anything. Such as "我可以教你" . it means :I can teach you. Of couse, it also can not combine with anyone or anything. "我教!" it's used at some suitations, like someone askes who can teach me? You can say "我教",it means I teach you,but you can omit object.
Second, "教给" When you want to teach somebody, you should say the exact object. You need use"教给".
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Oh,I must add one more point , "教给" usually use a sentence like this “教给某人(某事)”in parentheses :What you want she(or he)to learn some things– bByCommented Aug 11, 2019 at 13:25
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1you can click "edit" under you answer to edit your post and add the additional information you put in the comment here.– Mou某 ♦Commented Aug 11, 2019 at 13:35