Depending on which ever service you have access to, for example Ancestry, the best thing to do is
a) look at census records and see what information those give about where William Richard Clarke was born.
b) look for marriage records, such as banns which might give further information. In Williams case, I found banns that gave his fathers name.
I did have a quick look and built a simple tree, based on that information. If I've got the right person, it does seem that William was born in Liverpool, as others have said, but that both his parents were born in Ireland.
I can share more if you want, but I wasn't sure if you just wanted to do it yourself.
