AMD Piledriver FX 4350 4.3ghz Quad Core 12mb Cache
1tb Sata Hard Drive
8gb DDR3 1600 Memory
CIT Reaper Black Mesh fronted Case
24x Dual Layer Sata DVD Writer
ATI Radeon 6670 2gb DDR3 with HDMI Hyper Memory Upto 3.8gb
Windows 8 64bit With Disc and License will i be able to play games that are for ps4 without lag
Believe me, you should better get a PS4 rather than going for that PC. The 6670 does not even come close to the PS4's graphics at all. So you should better go for the PS4 instead of going for this. The PS4 is new and it should have no problems running games for the next 4-5 years without any problem at all at good eye pleasing settings wheras with this configuration you can barely run games at 720p medium.
Also, if you are sure that you want to build a PC, then tell us your budget. We are pretty sure that we might be able to build a better build for you for the budget you want to go for. So yeah, tell us the budget.