The command that displays the contents of a gzip compressed tar archive is tar ztf archive.tgz. This command uses the following options:

-z: Tells tar to read or write archives through gzip, allowing it to work on compressed files directly. -t: Lists the contents of an archive without extracting it. -f archive.tgz: Specifies the name of the archive file.

The output of this command will show the names of the files and directories stored in the archive, one per line. For example, if the archive contains three files named file1, file2, and file3, the output will be:

file1 file2 file3

The other commands are incorrect for the following reasons:

gzip archive.tgz | tar xvf -: This command will decompress the archive using gzip and pipe it to tar, which will extract the files to the current directory. The - option tells tar to read the archive from the standard input. This command does not display the contents of the archive, but rather extracts them.

gzip -d archive.tgz | tar tvf -: This command is similar to the previous one, except that it uses the -d option for gzip to decompress the archive instead of compressing it, and the -t option for tar to list the contents instead of extracting them. However, this command is redundant and inefficient, as tar can handle compressed archives directly with the -z option. Also, the -d option for gzip will delete the original archive file after decompression, which may not be desirable.

tar cf archive.tgz: This command will create a new archive named archive.tgz from the files and directories given as arguments. However, this command does not use the -z option, so the archive will not be compressed with gzip. Also, this command does not display the contents of the archive, but rather creates it.