I'm replacing my single sink vanity with a double sink vanity. Can I use the water supply lines that were for the single sink for the 2 new sinks. What do I use to supply both sinks?

Yes you will have enough water to supply both sinks. You can use a 3/8 inch plastic to connect the water to the faucets. The plastic is called pex pipe.

Try using an Add-a-tee adapter (http://hectorshardware.com/444059.html). Get two of them, and put one on the hot valve, and one on the cold valve. Then run supply hoses to each sink (total of four supply hoses).

You can obtain Add-a-tee's from the Link I provided, or you can simply wander over to Lowe's - that's where I bought mine.

Good luck!
Moishe
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By the way, if you indeed decide to buy from hectorshardware.com (the link I provided), make sure to get item #444068 - the one in my link has one of the outputs at a slightly different size; the one you need is 3/8 x 3/8 x 3/8.