How would you say 16 and 18 with the counter mai? My textbook [Japanese from zero 1, George Trombley] gives 6 and 8 as roku mai and hachi mai. But then gives 16 and 18 as juu rommai and juu hammai. Is this correct ? I am only learning but it sounds wrong to me. I would imagine it would be juu roku mai and juu hachi mai. If so then does 26/28, 36/38, etc. follow the same pattern ?

As you noted, 6 should be read as , and 8 should be read as .

Similarly, 16 should be read as , and 18 should be read as .

I have no idea why your textbook would render these as and . Neither pronunciation is correct -- these aren't even dialectal variants, so far as I'm aware; they're just wrong.

PS: The larger numbers you asked about, like 2628 etc, would still use the standard pronunciations.