How do I use gunzip and tar to extract my tar.gz file to the specific directory I want?

You can do a single tar command to extract the contents where you want:

tar -zxvf path_to_file -C output_directory

As explained in the tar manpages:

-C directory, --cd directory, --directory directory

In c and r mode, this changes the directory before adding the following files. In x mode, change directories after opening the archive but before extracting entries from the archive.

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As you added that you are using Solaris, I think you could try:

gunzip -dc path_to_file | tar xf - -C path_to_extract

Does this do what you want?

tar xzvf file.tar.gz -C /target/directory