How to decide cut off? I will try my best to explain this simple doubt that I have. I have three responses (Increased, decreased and no change) and I have calculated the percentage for each. For instance, for X case- 46% showed an increase, 34% showed a decrease and 20% showed no change (similarly I have 12 such cases); now to state that 46% is a significant increase, how can I decide that? Or in some cases, it is a 46% increase, 47% decrease and 17% no change. Kindly guide.

If you want to analyze X case separately from the other cases, you will probably want to use something akin to a one-sample sign test.  You will want to compare the counts of e.g. "increase" and "decrease" to null counts.
You might want to ignore observations of "no change" and simply compare counts of "increase" and "decrease" to a 50% / 50% split of counts.  That is, if you had 12 increase, 10 no change, and 3 decease, you would compare 12 out of 15 with either a binomial test or a chi-square goodness of fit test. In R, binom.test(12, 15) or chisq.test(c(12, 3)).
Depending on your purpose, you might consider an analysis that includes counts of "no change" along with those of "increase" and "decrease".  You might group them: "decrease + no change" vs. "increase".  Or you might use all three counts.
If you want to analyze X case with e.g. Y case, Z case, and so on, you might look at logistic regression, for either a binomial dependent variable or a multinomial dependent variable.
