Synecdoche-this is a figure of speech in which you use use part of a thing to represent the WHOLE thing: Example: "hired hands" for "workmen" (hands are just a part of the workmen).
Metonomy-this figure of speech is similar, in that you represent something by referring to SOMETHING RELATED TO IT. Example: "You must pay the crown its due"--in this case, crown refers to a king.
The terms are not opposites, but they are often misunderstood to be. The best way to tell the difference is to remember that with synecdoche, you substitute a part of a thing for a whole thing. In metonomy, you substitute a something associated with a concept or thing to represent the concept or thing.
Metonymy is a figure of speech in which a thing or a concept is called not by its own name but by the name of something that is closely related to it. For example, we might see the following sentence in a newspaper: "The White House has decided to close the prison at Guantanamo Bay." We know that the physical White House did not make this decision but that the President of the United States did. Because the White House is so closely associated with the president, we sometimes use the words interchangeably.
Synecdoche, then, is a specific type of metonymy in which the name for a part of something is used in place of the name for the whole thing. For example, the common Navy phrase "All hands on deck." This phrase means that all people (not just their hands) should report to the deck of the ship. Another example might be "you have hungry mouths to feed." Obviously, you are feeding more than the mouths, you are feeding the entire person.