Note that even numbers are all divisible by 2. Examples are:

`2, 4 , 6 ,8 , 10, 12, 14, 16, 18, 20...`

Then, let's try to determine which of these even numbers would result to an odd quotient when divided by 2. Note that odd numbers are not divisible by 2.

`2-:2=1`                    `4-:2=2`

`6-:2=3`                    `8-:2=4`

`10-:2=5`                 `12-:2=6`

`14-:2=7`                 `16-:2=8`

`18-:2=9`                 `20-:2=10`

So,  2,6,10,14 and 18 are the even numbers that when divided by 2 result to odd numbers.

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Therefore,

                      `2 + 4n`     (where n is an integer)

are the even numbers that when divided by 2 result to an odd quotient.