Question

Nitrogen dioxide reacts with SO2 to form NO and SO3:

$$NO2​(g)+SO2​(g)


NO(g)+SO3​(g)

An equilibrium mixture is analyzed at a certain temperature and found to contain [NO2] = 0.100 M,
[SO2] = 0.300 M, [NO] = 2.00 M, and [SO3] = 0.600 M. At the same temperature, extra SO2(g) is added to make a total [SO2] = 0.800 M.

Answer 1

I don't get the $ signs or the $$ signs. Nor do I see a question. I presume that the question is to determine the equilibrium concentrations after the SO2 concentration is changed form 0.300 to 0.800. Here is how you do that. I will delete the $ signs and balance the equation.
.................NO2​(g)+SO2​(g) ==> NO(g)+SO3​(g)
E...............0.100.......0.300...........2.00......0.600
[NO2] = 0.100 M,

First determine Kc. Plug those equilibrium numbers as shown into Kc expression as shown here. Kc = (NO)(SO3)/(NO2)(SO2)
Kc = (2.00)(0.600)/(0.100)(0.300) = 40
Next we redo the equation to show the new concentrations at THE NEW CONDITIONS AS INITIAL and finish the ICE chart.
.................NO2​(g)+SO2​(g) ==> NO(g)+SO3​(g)
I...............0.100.......0.800...........2.00......0.600
C...................-x..........-x................+x...........+x
E...............0.100-x....0.800-x.......2.00+x......0.600+x
Now plug the E line into the Kc expression and solve for x, then evaluate each of the reactants and products concentrations.
Post your work if you get stuck.