To solve the local Wordpress install only shows a home page, all other pages Not Found error there are many ways some of the important ways are as follows:-
The first thing you can do is go into Settings >> Permalinks >> and click "save changes" without changing anything.
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If the above step will give you .htaccess file permission issue, then you need to set privilege of your ROOT folder (where your wp-content folder lies) to read and write.
After setting the privilege of your ROOT folder again go and follow the same step I am mentioning below:-
Settings >> Permalinks >> and click "save changes" without changing anything.
Another thing you can enable rewrite_module. If you are on windows wamp then follow these click on wamp -> Apache ->Apache Module -> check rewrite_module.
Any of these two solutions will be helpful.