It's all in the wording

Let the number be x

Now when its multiplied by twice of it ie. 2*x, we get the following equation

2*(x)^2=162

x*x=81

since x is positive,

x=9

Let $x$ represent the number.

Therefore $x\times2x = 162$ .

$2x^2 = 162$

$x^2 = 81$

There are two solutions to this equality: $-9$ and $9$ . However, the question states that the number must be $>0$ . This eliminates $-9$ as a possible answer.

Checking for $9$ :

$9\times2 = 18$

$9\times18 = 162$

The answer is $\boxed{9}$ .