a few months; several months
Used to express an indefinite number of months, typically a small number. The か at the end adds the meaning of 'some' or 'a few'.
I lived in Japan for a few months.
This project will probably take several months.
Combination of 何 (nan, 'what') + counter ヶ月 (kagetsu, 'months') + か (ka, question/indefinite marker). The ヶ is a simplified form of 箇 (ka), a counter for items.