Initial concentration of the reactant is $1.0\mathrm{M}$. The concentration becomes $0.9\mathrm{M},0.8\mathrm{M}$ and $0.7\mathrm{M}$ in 2 hours, 4 hours and 6 hours respectively. Then the order of reaction is

A zeroth-order reaction is one whose rate is independent of concentration; its differential rate law is rate = k. We refer to these reactions as zeroth order because we could also write their rate in a form such that the exponent of the reactant in the rate law is 0:

rate=−$\frac{∆\left[\mathrm{A}\right]}{∆\mathrm{t}}$
=k[reactant]⁰
=k(1)
=k
so, here in first case rate =(1-0.9)/2 = 0.05

In second case rate=(1-0.7)/6 = 0.05

In third case rate=(1-0.8)/4 = 0.05

Rate constant value for Zero order reaction is constant
So given example is of zero order reaction.