How many integers from 42 to 92, inclusive, have a remainder of 4 when divided by 6

If they have a remainder of 4 when divided by six the sequence of terms are: 6n+4

42≤6n+4≤92

subtract 4 from both ends

38≤6n≤88

divide both ends by 6

6.3≤n≤14.6

since n must be an integer ...

7≤n≤14 so the number of integers is:

14-7+1=8

they are 6n+4 for n=[7,14] ... 46,52,58,64,70,76,82,88