Question

which one is correct? I would like to change my planning during the next days/in the next days/during the following days/during the days to come/during the next days to come/during the coming days.

Answer 1

I'm not sure of your question, but I think you mean "I would like to change my plans for the next few days", or you may have meant "I would like to change my plans in the next few days". I hope you can see the difference between these.

None of the other constructions sounds right: during the next days/in the next days/during the following days/during the days to come/during the next days to come/during the coming days.

If you were setting a specific deadline you could say for instance

"I need to buy some new shoes in the next three days" (before a fixed date)

"Our TV licence runs out in four days' time" (on a fixed date)

"During the next week I shall be eating lots of cheese because I bought too much" (continuous period of time)

I hope this helps.