Let $x_1, x_2, x_3, ......x_n$be the observations

$\therefore$Mean $=\frac{x_1+x_2+x_3+.....+x_n}{n}$

$\therefore 10=\frac{x_1+x_2+x_3+......+x_n}{n}.....\left(1\right)$

Now when observations are multiplied by $2,$then new observations are

$2x_1, 2x_2, 2x_3......., 2x_n$

New mean $=\frac{2x_1+2x_2+.....+2x_n}{n}$$=2\left(\frac{x_1+x_2+.....+x_n}{n}\right)$

$=2\times 10$

$=20$