This is coming out of Mumford's GIT, section 7.2, page 131.

$A/S$ an abelian scheme of dimension $g$ with polarization $\bar{\omega}$ of degree $d^2$. Then $\pi_*(L^\Delta(\bar{\omega})^3)$ is locally free on $S$ of rank $6^gd$ which defines the closed immersion $\varphi_3 : A \rightarrow \mathbb{P}(\pi_{*}(L^\Delta(\bar{\omega})^3))$. Equip this with a linear rigidification $\phi : \mathbb{P}(\pi_{*}(L^\Delta(\bar{\omega})^3)) \rightarrow \mathbb{P_m} \times S$ so that we get an embedding $I : A \rightarrow \mathbb{P_m} \times S$.

Mumford then states the Hilbert Polynomial of $I(A)$ is easily computed to be $P(X) = 6^gdX^g$.

Exactly how does one go about finding this Hilbert polynomial?