= Solution
Here three means the total spacetime dimension. A dimensionless <action> requires $[\mathcal L]=3$ in <mass dimensions>. The <kinetic term> gives $2+2[\phi]=3$, so $[\phi]=1/2$. Matching the <mass dimensions> of both <field interaction terms> gives
$$
\boxed{[g_1]=3-4[\phi]=1,\qquad [g_2]=3-6[\phi]=0.}
$$
Thus $g_1$ has units of <mass> and $g_2$ is dimensionless. The quartic interaction is superrenormalizable by <power counting>, and $g_2$ is a <marginal coupling> by <power counting>.
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