An algebra problem by Gilang Ardya

Let

$x=0.66666..$ $\implies$ $10x=6.66666...$

Now : $10x-x=6.66666...-0.66666... =6\\ \implies 9x=6$

So, $\color{#20A900} {x=\dfrac{2}{3}}$

So, $27\times x=\dfrac{2}{3} \times 27=\color{#3D99F6} {\boxed{18}}$

0.666666......=2/3: Therefore, 0.666666......x27 = 2/3 x 27 = 2x9 =18

0.6666... = 2/3

2/3*27= 18

0.666.....x27=(2/3)x27=2x9=18

0.66..=2/3, so

2/3 * 27/1 = 2/1 * 9/1 = 18/1 = 18

0.66666.......=2/3

2/3*27=18

0.666... = 2/3

So, (2/3)*27 = 18