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Phenobarbital (5-ethyl-5-phenylpyrimidine-2,4,6(1H,3H,5H)-trione)

If you carefully look into this strucuture, you will see that carbon of the pyrimidinone ring have ethyl and phenyl substituent at C-5 carbon. (numbering of the pyrimidinone ring is such that it starts from one of the ring N and goes towards other N so that Nitrogens are at 1 and 3 positions and having C=O carbon at 2 position)

Now just consider a plan passing through the positoin 2 and 5 of this ring. In such a case ethyl and phenyl group will lie on to this plane and the two N and two C=O carbons are at opposite side of the plane as that of the mirror images.

So this is the plane of symmerty which cuts the Phenobarbital into two equal symmetric halfs, and therfore this compound is Achiral.

(Any compound with a plane of symmetry of an axis of symmetry is ACHIRAL)

I hope this will help.