I want to check the effect of an inhibitor on the desired gene expression in my cell line. After how much time should I isolate the RNA and check the expression; after 6hour, 12hour, or 24 hour?
You'll need to run a time course assay harvesting at several intervals to find the most appropriate time point for your assay. Every inhibitor has different kinetics for how it will perturb a signal transduction pathway, and the stability of different genes (both mRNA and protein) has a major impact on the rate at which gene expression metrics respond to a particular perturbation. So-called "early response genes" can show changes in mRNA abundance in 30 minutes or less after a stimulation. Other genes may take hours to days to respond.
In addition to checking multiple time points (maybe 1hr, 4hr, 8hr, 16hr, 24hr, 48hr), you should consider assaying both mRNA and protein levels, if suitable reagents exist. Changes in gene expression at the mRNA level do not always correlate with changes in protein abundance, and vice-versa. Much depends on the mechanism of action of your drug, and particular features of transcriptional/translational/post-translational control of your target gene(s).
Just to add to the comments by Daniel and Jonathan, you might also consider to try different concentrations of your inhibitor in this assay. High concentrations might induce some unspecific side effects.
you can not generalize this effect and predict the exact time interval for gene expresssion analysis after some treatment, because it may be different in different cases, But in most cases I have seen in various research papers it is 24 hrs after treatment. so I may suggest you to start your experiment with 24 hr interval if you are lucky enough you may shoot the target in first instance Otherwise you have to change the gap period according to your pilot study as suggested by daniel, or you can also reffer to to some reference articles who are already working on gene of your interest, I am sure you will get good clue from that.