These expressions have similar meanings.
I don’t time what time I will arrive. Anyway / anyhow / at any rate I will certainly be here before seven o’clock.
We were late, anyway / anyhow the film wasn’t very good.
What a horrible experience! Anyway / anyhow / at any rate, you’re safe, that’s the main thing.
We have to win this contract at any rate.
Anyhow can be used as an adverb. It means ‘by one means or another’ ‘carelessly’ or ‘without order’.
The door was shut and I couldn’t open it anyhow.
The work was done all anyhow.
Note that ‘anyway’ does not mean the same as ‘in any way’ which means ‘by any method’.
Can you help me in any way?