The total number of eight - digit landline telephone numbers that can be formed having at least one of their digits repeated is:

Total 8 digit number which can be made using all digits when repetition is allowed = $$9*10^7$$ = $$90000000$$

Total 8 digit number which can be made using all digits when repetition is not allowed = $$9*9*8*7*6*5*4*3$$ = $$1632960$$

Therefore, The total number of eight - digit landline telephone numbers that can be formed having at least one of their digits repeated =  $$90000000$$ - $$1632960$$ = $$88367040$$.  Hence the correct answer is None of the above (D).