I have a folder and I wonder how I can use icacls.exe to set its permissions to be special for a certain user so it looks like below?
That's like the 'modify' permission set, except you've swapped 'Delete' for 'Delete subfolders and files'. You can grant these individually starting e.g. from the read-execute permission set
icacls folder /grant domain\user:(RX,WD,AD,WA,WEA,DC)
or /grant:r
if you want to overwrite rather than add to any existing permissions.