No, every positive integer cannot be of the form 4q + 2, where q is an integer.
Justification:
All the numbers of the form 4q + 2, where ‘q’ is an integer, are even numbers which are not divisible by ‘4’.
For example,
When q=1,
4q+2 = 4(1) + 2= 6.
When q=2,
4q+2 = 4(2) + 2= 10
When q=0,
4q+2 = 4(0) + 2= 2 and so on.
So, any number which is of the form 4q+2 will give only even numbers which are not multiples of 4.
Hence, every positive integer cannot be written in the form 4q+2