measure the inside of the cabinet, wall to wall. goto Lowes and say I need a 1x6 cut to that length and some #8 2 inch wood screws and a dill bit for those screws, they will know what you need.
Also, you see the 4 screw holes on the back of your monitor? you need to find machine screws, again at Lowes, that will fit those holes, get them in two inch and handful of washers for those bolts.
Screw the 1x6 to the inside of your cabinet to the beams that the bezel sits on. then drill holes in the wood, for the mounting holes on the back of the monitor then mount the monitor and voila.
Be sure to drill pilot holes in before you put any bolts or screws in any wood.