hello,

I have created 2 users(mark and david) and a directory named project.
I wanted to enable other user to travel through ~ to access ~/project and I'm not sure how to enable it them to access, so what command would I use to achieve this?

using cent os7

The usual soln is to create a user & group called 'projectname' and chmod g+s the dir.
Add all relevant users to group projectname.
The chmod ensures that any files created by any (group) user will inherit the containing dir's group ie projectname, so will be available to all group members.

Its NOT recommended to give others access to your $HOME (ie '~' )

if i were to use hardlinks what whould i have to do? if i have or allow that user have the permissions?

another question, when i long list that user account home root ls -ld ~ and the output came out with
drwx-----x. 6 david david 4096(I made that x permission to others. so that other user(mark) can access through the hardlink, but i still don't know how to enable others to travel through) and i was wondering how would the user group ownership david change to music, I guess i have to change mark's group ownsership to music as well. so that both can access the ~/project? using chgrp but i dont know what synthax.... haha

or is it usermod -aG music david? on the root? to make david music

English is not my mother tongue, but I think your sentence "when i long list that user account home root" is ungrammatical and doesn't make sense.

What do you mean by access through the hardlink? Which hardlink?
mark will be able to cd to this directory but not read it, so that it is essentially inaccessible to mark.

I think chrism01 nailed it. What s/he describes is sometimes called "user private group scheme". Google for it and implement it.