How to Resize a Disk Partition in Disk Utility?

You can only change the size via the end of one partition, not via the start of a partition, thus you have two choices (maybe three, if you are willing to pay more money for it).
Make the unformatted space before the Snow Leopard partition into an extra partition to have a data partition or whatnot, or get hold of an external HDD, properly formatted (GUID as partition scheme, Mac OS Extended (Journaled) as format), use CarponCopyCloner (version 3.4.4 should suffice) to make a clone of the Snow Leopard partition onto the external HDD, boot from the external HDD via holding down the Option key after the startup sound, format the internal HDD completely via Disk Utility like you did with the external HDD, then use CarbonCopyCloner to clone the external HDD to the internal HDD and again boot from the internal HDD.
Or you could buy some partition software like iPartition and others to reorganise the partition schematics.

I don't believe you need an external drive.

Assuming that the first, now-empty partition is large enough, just use CarbonCopyCloner to clone the contents of the second (Snow Leopard) partition to the first (empty) partition.

Once done, you will have -2- partition with Snow Leopard. (suggestion: give the first partition a distinctive name, so you will be able to distinguish between it and the other SL partition)

Use Startup Disk to set the first partition as your boot p. Then reboot.

Once rebooted, check to be sure the clone is "as you like it", then, delete the -old- Snow Leopard partition (the second one down).

I can see this going one of two ways:
1. It may be possible to simply delete the partition (and all the contents along with it), or…
2. You may first need to delete the contents using the finder, then use Disk Utility to remove the partition

When done, you should have one partition, with all of its contents toward the physical "beginning" of your drive.

I've cloned one partition to another on the same drive before, no problems at all.