Number of divisors of the form $4n+2 ,(n\ge 0)$ of the integer 240 is

$240=2^4\cdot 3^1\cdot 5^1$

$\therefore$ Number of divisors of 240 are 

5 x 2 x 2 = 20 as listed below

$\begin{array}{l}1,2,4,8,16=\left(2^0\cdot 2^1\cdot 2^2\cdot 2^3\cdot 2^4\right)\cdot 1\\ 3,6,12,24,48=\left(\right)\cdot 3\\ 5,10,20,40,80=0.5\\ 15,30,60,120,240=\left(\right)\cdot 3\times 5\end{array}$

But only 2, 6, 10, 30 of column (2) correspond to the form

$4n+2\text{ for }n=0,1,2,7$