How do you shell expand your variables and why?

@zephyr echo "${HOME}/docs"

This is the best way. It's also the way the Shellcheck ~~wants~~ sometimes recommends.
- @bloopernova As you mention it, here the links for anyone interested: Online tool https://www.shellcheck.net/ and you can install it locally too https://github.com/koalaman/shellcheck .
- This isn't true. Shellcheck doesn't insist on braces unless it thinks you need them.
This is the way
I also do this so the variables are more easily spotted.
This is the right way
This has never stuck with me, and I hadn't thought about why until now. I have two reasons why I will always write ${x}_$y.z instead of ${x}_${y}.z:
Syntax highlighting and shellcheck have always caught the cases I need to add braces to prevent $x_ being expanded as ${x_}.
I write a lot of Zsh. In Zsh, braces are optional in way more cases. "$#array[3]" actually prints the length of the third item in array, rather than (Bash:) the number of positional parameters, then the string 'array[3]'.
- @gamma I just use them out of consistency and principle, so I don't need to think in which case it is required or not.
- I will always write ${x}_$y.z instead of ${x}_${y}.z:
  The difference between the two seems different to what's in the OP. Is there a typo here?

find “$(echo $HOME > variable_holder.txt && cat variable_holder.txt)/$(cat alphabet.txt | grep “d”) $(cat alphabet.txt | grep “o”)$(cat alphabet.txt | grep “c”)$(cat alphabet.txt | grep “s”)”

This is the easiest method

when you're paid by character written
This really enterprises my bash.
@ilegadh You don't need cat in cases when grep "d" alphabet.txt can read from file too. Edit: But obviously your comment was more of a joke to over complicate it. So never mind then.
- To be safe, should probably output grep to a file, then cat that.
What should I search to better understand what is written here? Don't mind learning myself, just looking for the correct keywords. Thanks!
- This comment is a joke and you wouldn't want to do it like that in reality, but here are some related keywords you could look up: "Unix cat", "Unix pipeline", "grep", "output redirection", "command substitution".
- Read the Bash manual. That one patter on the GP is called "Command Substitution", you can search for it.
- ExplainShell should help

First one, then the other, then I forget the quotes, then I put them in single quotes by accident, then I utilize that "default value" colon syntax in case I'm missing HOME , then I just stick to ~ for the rest of the file.

Typically find "$HOME/docs", but with a few caveats:

In Zsh or Fish, the quotes are unnecessary: find $HOME/docs
If I'm using anything potentially destructive: mv "${HOME:?}/bin" ...
Of course, if it's followed by a valid identifier character, I'll add braces: "${basename}_$num.txt"

I do what the linter tells me to: https://github.com/koalaman/shellcheck