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Look at this sentence:

  • next, we explain why the problem will be done this way.

Could we write the sentence adding the preposition "in" to?

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    To do a problem does not make sense unless you mean to do a math problem. Then, it's to do a problem this way. Otherwise, to solve a problem in this way.
    – Lambie
    Sep 9, 2017 at 12:43
  • Yes, you are right, i saw this sentence in a mathematic book. I want to know when to use "this way and in this way" and which one is. Correct. @lambie
    – user59167
    Sep 9, 2017 at 14:02

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Both ways are fine. (math context)

Next, we explain why the problem will be done in this way.

This would be considered more formal. However, the in can be implied as in your example, thinking of it as follows. ( ) adds implied information.

Next, we explain why the problem will be done. (How?) This way.

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  • How do you do this math problem? Answer: Do it this way. [as the person answering writes on a screen or sheet of paper]. Do it "in this way" would be incorrect here. However, one does solve a problem in this, that or some way.
    – Lambie
    Sep 10, 2017 at 15:09

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