Understanding Errors During npm Installation

As @cubick commented on the error message, while running npm install from C:\Program Files\nodejs\node_modules\npm, create the folder in the C:\Program Files\nodejs\node_modules\node_modules.code.

As a countermeasure, we will refer to these articles, including those introduced in the comments:
Create Node.js Project
npm Common Command Summary
Basic Usage for npm
When you are not allowed to do npm install

Try it.

"By the way, the ""Create Node.js Project"" introduced the following guidelines, which are not limited to Node.js/npm, but also for other programs."

Also, when creating a directory, be careful not to include either a Japanese string or a blank in the path. Recently, I don't often encounter Japanese strings (full-width characters) and spaces, but I avoid them because they often cause unexpected problems.

In addition, when creating and selecting folders/directories for work (unless explicitly covered by some instructions):

• Folder protected by the system and requiring administrator privileges for access
  For example, C:\Windows, C:\Program Files, C:\Program Files (x86), C:\ProgramData and the folder under it, and the root folder for each drive, such as C:\
  Alternatively, when you click on Explorer, "You do not have permission to access this folder. US>Click Continue to obtain permanent access to this folder (even if you have obtained access with it, you should not use it)
• Folder where other programs are installed, folder where other programs are using it for work
• Folder such as desktop download pictures.(Maybe the document is not good enough?)