Bayesian network calculation to find probability for independent events?

I have the following Bayesian network:

I'm having trouble understanding how to calculate some of the conditional probabilities between nodes, in particular when they are independent. For instance, how would you calculate P(C=true, G=true|H=false)? I'm aware that I have to use the Bayes rule and the conditional probability formula. How do you go about setting up the equations for each of these and do you use variable elimination for any of these?