truthTable=Table[ 
Sum[Signature[{l,m,p,q}] Signature[{l,m,i,j}],{l,1,4},{m,1,4}]==2(KroneckerDelta[p,i]KroneckerDelta[q,j]-  KroneckerDelta[p,j]KroneckerDelta[q,i])
 ,{i,1,4},{j,1,4},{p,1,4},{q,1,4}];

tTable = Flatten[truthTable]

Length[tTable]

Count[tTable,True]

Sum[Signature[{l,m,i,j}] Signature[{l,m,i,j}],
{l,1,4},{m,1,4}
 ,{i,1,4},{j,1,4}]