find the common difference of an arithmetic sequence whose second term is 6 and whose sixth term is 30

First: Since you know the value of the second term and the value of the sixth term, count the number of steps from 2 to 6 (which is 4: from 2 to 3, from 3 to 4, from 4 to 5, and from 5 to 6).

Second: Find the distance from 6 to 30:  30 - 6  =  24

Third:  Divide the distance by the number of steps:  24 ÷ 4  =  6.  The common diference is 6.