何 + [counter] + か
The pattern 何 + [counter] + か is used to express an indefinite quantity – "some," "several," or "a few" of something. By placing か after a counter word preceded by なん何 (なん), the speaker indicates that the exact number is unknown or unimportant.
This is similar to saying "some number of ~" in English. The counter changes depending on what is being counted, just as it normally would.
This pattern implies a small to moderate number – not a large amount. If you want to express "many" or "a lot," you would use different expressions like たくさん or いくつも. The feeling is closer to English "a few" or "several" rather than "many."
Note the difference from いくつか, which also means "some" but does not specify a counter. 何 + [counter] + か is more specific about what kind of thing is being counted.