from what I can decipher from your attempts , your initial error beginns here :
[tex][HI]_{eq.}^2 = \left( \frac {0.120}{0.5} \right)^2 = \color{red}{ 0.0576 \neq 0.21} [/tex]
... though this is irrelevant, as you can't calculate [HI]eq. in this manner from c0(HI)
a much better idea would be to set up a LMA expression, and fill in what you know:
[tex] K_c = \frac {[H_2] \cdot [I_2]}{[HI]^2} = \frac { x \cdot x }{(c_0(HI) - 2x)^2} = 2 \cdot 10^{-2}[/tex]
resolve for x , calculate n(I2) thereof
regards
Ingo