= Solution
All daughter <particles> are massless, so the parent <mass> $M$ supplies the only kinematic scale at <tree-level Feynman diagram>[tree level]. Each vertex has two derivatives, making its <scattering amplitude> scale as $\lambda_iM^2$. For the four-$b$ vertex, symmetrizing over the derivative-bearing legs yields a sum of pairwise <four-momentum> products, which is proportional to $M^2$ by <four-momentum conservation>.
For $n$ massless daughters, the <Lorentz invariance> <Lorentz-invariant phase-space measure> scales as $M^{2n-4}$: each $d^3q/(2E)$ contributes two powers and the four-dimensional <Dirac delta> removes four powers. Including the parent factor $1/(2M)$ gives $\Gamma\sim|\lambda_i|^2M^{2n-1}$. Thus
$$
\boxed{\Gamma_{aa}\propto|\lambda_a|^2M^3,\qquad
\Gamma_{bbbb}\propto|\lambda_b|^2M^7,\qquad
\Gamma_{\gamma\gamma}\propto|\lambda_\gamma|^2M^3.}
$$
The unspecified factors are dimensionless angular integrals and identical-particle factors. Each result has <mass dimension> one, as a <decay width> must in <natural units>.
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