"Somehow" would be used in a sentence like"He will do it somehow", meaning he will find a way to do it. "Anyhow" is used in sentences like, "he didn't want to do it anyhow", where anyhow means "anyway", meaning he didn't want to do it. Typically, you see a pair of sentences like, He missed his chance to go to the play. He didn't want to go, anyhow.