How to install older version on carthage

1) First of all be sure to remove everything:

brew uninstall --force carthage

2) Then search the commit that you like from here:

https://github.com/Homebrew/homebrew-core/search?p=2&q=carthage&type=Commits&utf8=✓

3) in your case might be this:

https://github.com/Homebrew/homebrew-core/commit/f74d9ba598c9843552450abeb382cacd0e71d4c0

the one related to Carthage v0.24, which should be compatible with your requirement of working with Xcode 8.3.3.

4) then get the commit identifier f74d9ba598c9843552450abeb382cacd0e71d4c0 and run:

brew install https://github.com/Homebrew/homebrew-core/raw/f74d9ba598c9843552450abeb382cacd0e71d4c0/Formula/carthage.rb