The Monstrum Tactical Extended Quad Rail with A2 Front Sight Post Cutout will not install out of the box on the Ruger AR556.  We do not support the use of the rail on this rifle.
However the rail will install on the rifle with a slight modification.
The issue with the Ruger AR556 is the bayonet lug on the bottom of the barrel extends further than standard AR-15's and obstructs installation of the front bottom rail section.
Ruger AR-556 Bayonet Lug
The modification will involve filing down the third rail section so that it will fit in place to the front of the bayonet lug.  You will need to file down or cut off approximately 10mm from the rear (the end toward the barrel) of the rail section
Quad Rail with A2 FSP Cutout Ruger AR-556 Modification
I have posted some pictures, provided by one of our customers, of this modification.
Ruger AR-556 Extended Quad Rail with A2 FSP Cutout
Ruger AR-556 Quad Rail with FSP Cutout Modification
Please note that modification of the rail will void your quad rail warranty.