Synergic bonding involves transference of electrons from ligands to metal. The transference of electrons takes place from filled metal orbitals to anti-bonding orbitals of ligands. It is a bond between a carbonyl group acting as a ligand and a metal. Synergic bonding means self strengthening bond. More the number of d electrons on the central metal ion more the synergic bonding. In metal carbonyls' oxidation state of the metal is zero.
In the complex [Mn(CO)5], the electronic configuration of Mn is 3d54s2. As carbon monoxide is a strong field, pairing of electrons occurs. Hence, the new electronic configuration of Mn is 3d7.
In the case of [Mn2(CO)10] also electronic configuration after pairing of electrons is 3d7.
In the complex [Cr(CO)6] , the electronic configuration of Cr is 3d54s1 . As carbon monoxide is a strong field, pairing of electrons occurs. Hence, the new electronic configuration of Cr is 3d6
All of these compounds can show synergic bonding.