Unable to install on Mac M1(Sonoma 14.3.1)
Is this an older Homebrew installation held over from a previous Intel mac? The error about "not built for the x86_64 CPU architecture" makes me suspect that even though you are on an M1, the Homebrew installation is an Intel one.
which brew should return /opt/homebrew/bin/brew if it is the M1/ARM version. If not, re-installing from https://brew.sh should fix the problem, but let us know if the issue persists.

@marcprux I have installed tried both the commands brew update and install commands but still facing same issue
Very odd. You are using the M1 version of Homebrew, but it appears to be trying to install the x86 version of a dependency.
Can you try completely uninstalling Homebrew from the machine as per: https://github.com/homebrew/install#uninstall-homebrew
Once it has been removed, re-install it from scratch as per: https://github.com/homebrew/install#install-homebrew-on-macos-or-linux
And finally, try installing Skip again: brew install skiptools/skip/skip
Let us know if you still get the error…
Closing for now because we believe this was addressed, but feel free to re-open if there is more information.