The nitro-group is an electron-withdrawing group. The presence of this group in the ortho position decreases the electron density in the O-H bond . As a result, it is easier to lose a proton. Also,the o-nitrophenoxide ion formed after the loss of proton is stabilized by resonance. Hence,ortho-nitrophenol is stronger acid.On the other hand, methoxy group is an electron-releasing group. Thus ,it increases the electron density in the O-H bond and hence, the proton cannot be given out easily. Therefor ortho-nitrophenol is more acidic than ortho- methoxyphenol.