If you have only ever heard of Lewis diagrams,* then you might misinterpret the shown representation.
Instead of bonding the focus of this diagram is more on structure, even though it compromises on that when showing a double bond in the carbonyl moiety, and to show that this particular carbon has four closest neighbours.
You can almost instantly spot this as lone pairs are omitted completely.
I do not want to dive deep into the bonding of this complex, it is far better to consult the literature for this, but one way of looking at is to look at the ligand first.
A Lewis diagram of carbon monoxide is $\ce{^\ominus|C#O|^\oplus}$, which emphasises on the triple bond nature of the compound. There are other resonance structures. This molecule is very versatile and has many bond modi. One important feature is that it is a σ-donor through carbon.
Carbon monoxide bond in μ3-fashion to the iron cluster. This is a highly delocalised bond; a multi-centre-two-electron bond in first order approximation. The important take-away is that carbon still only utilises eight electrons for bonding.
In a more bonding complete diagram, there should be a lone pair and a positive formal charge at oxygen, a triple bond between oxygen and carbon, and a single line pointing to the middle of the vertex established by the iron cluster. Obviously you'll sacrifice some structural information. But diagrams do that anyway.
One more important point is, that you should not confuse valence with coordination. It is better to avoid valence all together, as its use has been and will remain inconsistent at best.
According to the IUPAC definition,† carbon is tetravalent. Always. It is a constant specific to this element.
Footnotes
* In a strict interpretation of a Lewis diagram, all electrons are shown and all lines represent two bonds. There is no difference whether these bonds covalent, ionic, or anything in between, there is no discrimination "from where the bond originates". There are no arrows in true Lewis diagrams.
† Valence in the Gold Book: https://doi.org/10.1351/goldbook.V06588
$\ce{\mu^3-CO-[Fe4(CO)12]^2-}$displayed inline as $\ce{\mu^3-CO-[Fe4(CO)12]^2-}$ or with double dollars to display it separately as $$\ce{\mu^3-CO-[Fe4(CO)12]^2-}$$ – Poutnik Feb 18 '22 at 07:53