Would my computer be able to run this modpack?

[SupremeStorm]

These are my specs: http://www.pcworld.com/product/788982/xps-8300-midsize-tower-desktop.html

Also, how much memory does it take up?

[iEmeraldGolem]

I believe most desktop PCs from the past few years can run this pack. You just need to allocate 2 GB of RAM. You need Java 64 bit to do this. If you have that already, use the cog wheel on the Technic Launcher screen to allocate more RAM.