The J statistic is a test of overidentifying restrictions, which checks whether the instruments you use are valid, i.e., uncorrelated with the errors. The Prob(J-Statistic) is the p-value of this test, which indicates the probability of observing a J statistic as large as or larger than the one you obtained, under the null hypothesis that the instruments are valid.

In your case, the J statistic value is 19.99 and the Prob(J-Statistic) is 0.45. This means that you cannot reject the null hypothesis that the instruments are valid at any conventional significance level. In other words, your results do not provide evidence against the validity of your instruments.

However, this does not necessarily mean that your instruments are truly valid. It is possible that your J statistic is low because your instruments are weak, i.e., they have low explanatory power for the endogenous variables. Weak instruments can lead to biased and inconsistent estimates of the parameters. Therefore, you should also check the relevance of your instruments by looking at their correlation with the endogenous variables or by using other tests such as the Cragg-Donald test or the Kleibergen-Paap test.

Good explanation.