DeleteCases[{{12, 1, 23, 4}, {0, 0, 0, 0}, {34, 67, 5, 60}, {0, 0, 0, 0}}, {0 ..}]
(* {{12, 1, 23, 4}, {34, 67, 5, 60}} *)
(* this also results in the same answer *)
Cases[{{12, 1, 23, 4}, {0, 0, 0, 0}, {34, 67, 5, 60}, {0, 0, 0, 0}}, Except@{0 ..}]
(* or *)
{{12, 1, 23, 4}, {0, 0, 0, 0}, {34, 67, 5, 60}, {0, 0, 0, 0}} /. {0 ..} :> Sequence[]
(* using select *)
Select[{{12, 1, 23, 4}, {0, 0, 0, 0}, {34, 67, 5, 60}, {0, 0, 0, 0}}, Total@#x !=\[Function] FreeQ[x, {0 &]..}]]
(* in fact select can be usedassuming inno thisnegative wayintegers *)
Select[{{12, 1, 23, 4}, {0, 0, 0, 0}, {34, 67, 5, 60},
{0, 0, 0, 0}}, x \[Function]Total@# FreeQ[x,!= {0 ..}]]&]