Technically, one needs a volume since M is substituted into the Kc expression and not mols. You don't have a volume listed. However, the volume cancels as follows:
Kc = (mols HI/v)^2/(mols H2/v)(mols I2/v). That means we can assume any volume or ignore volume (or use 1 L)
(H2) initial = 0.2
(I2) initial = 0.15
(HI) equilibrium = 0.26
........H2 + I2 ==> 2HI
I......0.2..0.15......0
C......-x....-x......2x
E...0.2-x...0.15-x...2x
but you know 2x = 0.26 and that allows you to evaluate mols H2 and mols I2.
Substitute the E line into Kc expression and solve for Kc.
Post your work if you get stuck.