Correct spelling, explanation: months is a plural noun. It was created by adding the -s letter to the end of the root (month), so it’s a regular one. This word originates from Old English mōnath, of Germanic origin; it’s related to Dutch maand and German Monat, also to moon. You can’t spell months as monthes because the singular ends in a -h.

Definition of months:
noun (plural), periods of about four weeks
The siege lasted almost four months.
He’s returning to Africa tomorrow after six months in Europe.

Collocations with months:
Some most commonly used collocations include: past few months, and previous months.
The past few months have been difficult for me.
Our company began to achieve better results compared to previous months.

Incorrect spelling, explanation: the word monthes doesn’t exist and this form should be avoided. The word-formation basis is correct, but the suffix is not. The right form is months with the -s. Why? Because the singular doesn’t end in –s, –sh, –ch, –x, or –z (for those letters you add -es). Try to remember that monthes is just a misspelling and you can’t write this word like that.