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What is the letter designation on coins for?

It's called a mint mark and identifies the mint that struck the coin. See the Related Question for more information.


Value of 1954 plain?

Plain what? If you're referring to U.S. coins there were 5 denominations struck that year so more information is needed. The best thing to do is to post a new question with the coin's denomination and condition.


What is the value of a 1964 penny that appears to be struck normally on both sides but is one-tenth of the thickness?

I modified your question because coins are struck or minted rather than "printed", which refers to books and banknotes. It's not possible to say exactly what happened without looking at your coin but my first guess is that it was exposed to some corrosive or acidic liquid. Because of the way copper "flows" when a coin is struck, the design will still appear clearly even when much of the metal has been dissolved. Unfortunately that makes it a damaged coin with no extra numismatic value. It's still an interesting curiosity, though.


What is the value of a double struck 1989 US quarter?

You'll need to provide more information. What kind of double-strike is involved? The same image twice on each side, but out of alignment? Opposite images on each side? Or on one side only?


What is the total mintage for 2009 dimes and nickels?

According to the US Mint, a total of 86,640,000 nickels and 146,000,000 dimes were struck for circulation in 2009. Those numbers were much lower than average due to the so-called Great Recession.