The given sentence itself is wrong. Your two alternatives are perfectly grammatically correct, save for a little error which we'll get to later.
"Not only... but also" is an example of a correlative conjunction. And when using correlative conjunctions, you have to make both parts of the conjunction parallel, meaning you have to make sure both parts have equal grammatical units. See here for more on parallelism.
For example, here's the given sentence:
When you read, you can not only {learn some new words}, but also {you can learn how to use these English words}.
You can easily see that the two {parts} aren't equal, or parallel. Here are some fixed versions, with the parallelisms sorted out:
When you read, you can not only {learn some new words}, but also {learn how to use these English words}.
When you read, you can learn not only {some new words}, but also {how to use these English words}.
When you read, not only {can you learn some new words}, but {you can also learn how to use these English words}.
You may have noticed that with the third one, the word order is kinda changed around, and this is the little error in your first alternative.
If you introduce an independent clause with "not only...," the clause has to be inverted, hence the "not only can you" instead of "not only you can." It's just how it is.
As for "but you can also" word order, the adverb "also" has to come after "be" or helping verbs. For more info about adverb placement, see here.
Cheers.