= Solution
Let brackets denote <mass dimension>. In <natural units>, $[x]=-1$ and $[\partial_\mu]=1$, so a dimensionless <action> requires $[\mathcal L]=D$. The <kinetic term> fixes
$$
2+2[\phi]=D,
\qquad
\boxed{[\phi]=\frac{D-2}{2}.}
$$
The <cubic scalar field theory> interaction then requires $[\lambda]+3[\phi]=D$, giving
$$
\boxed{[\lambda]=\frac{6-D}{2},\qquad D_c=6,\qquad[\phi]_{D_c}=2.}
$$
The <coupling constant (physics)> is dimensionless at this <critical dimension of a monomial scalar interaction>. For $D<6$ it has positive <mass dimension>, while for $D>6$ it has negative <mass dimension>, the usual <power counting> distinction between super-renormalizable and non-renormalizable cubic interactions.
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