What country? I guess the U.K. as it is £2
What games? Never heard of Eurogames, maybe Commonwealth Games
What year? If the above is correct, then maybe 2002 when four versions were issued.
This link says: The Spinks 2008 (six years old) catalogue price on this set is £240.00
This company is selling for £180 ...
http://weightoncoin.co.uk/index.php?main_page=product_info&cPath=4_53&products_id=1124&zenid=bf5dda49a270f2496c318e589f67f351
Quote: In 2002 the Royal Mint issued a very special set of four Silver Proof PIEDFORT two pound coins to commemorate the Commonwealth Games that were held in Manchester that year.
Each coin depicts one of the flags of the United Kingdom - England, Scotland, Wales, and Northern Ireland and are struck in silver to the highest proof standard. For the PIEDFORT set the flags on the coins were highlighted with colour, which is a very unusual step for the Royal Mint.
They are housed in their original wooden case with a gold plated medallion and certificate of authenticity / information booklet as issued by the Royal Mint.