I think the way to approach this would be to substitute some sample values of x.
Since x is an integer, i am going to use the following sample values:
-3,-2,-1,0,1,2,3
y=3x+2
x=-3, y = -7
x=-2,y= -4
x=-1, y= -1
x=0, y = 2
x=1, y = 5
x= 2, y = 8
x= 3, y = 11

since Choices are 4,5,6,7,8 : It is obvious that 4,5,7, and 8 are divisors of y, only 6 is not! Hence the answer is 6

factor or divisor means factor who completly divides the divisible
if we plug value lets say 4

y=3(4)+2
y=14 is not divisible by 4 ie remainder is not equal to 0.

2) y=3(5)+2
y=17 is not divisible by 5 ie remainder is not equal to 0.

similarly for the given values how can one judge about its non divisiblity
since all given values of x are not divisor.

I substituted values for x. Then I checked to see if the answer choice were factors of y.

I could easily eliminate all the values except 6.

This method works well from Problem Solving questions, but could lead to problems if this were a Data Sufficiency question.

For y = 3x + 2 to be divisible by 3 or any multiple of 3, it has to be divisible by 3

here 3x is divisible by 3
but 2 is not divisible by 3
hence 3x + 2 is not divisible by 3

or any multiple of 3 (6,9,....)