Files can be deleted from desktop, downloads, documents, and pictures in your H: Drive by selecting them (or highlighting multiple at once) then clicking on the giant RED X at the top that says "delete".
Open or create a new folder in Google Drive
To select multiple files at once, single-click hold your mouse button down, and drag over the files you would like to delete.
Go to G:\ Drive -- My Drive or Shared Drives
Open or Create a new folder (Open New Folder)
Paste them (Right click mouse, choose 'Paste' or ctrl V)