= Solution
In $d$ <spacetime> dimensions, $[d^dx]=-d$ and a dimensionless <action> requires $[\mathcal L]=d$. Since $[\partial_\mu]=1$, the canonical <kinetic term> fixes $2+2[\phi]=d$. The cubic and quartic terms then give
$$
\boxed{[\phi]=\frac{d-2}{2},\qquad[\kappa]=\frac{6-d}{2},\qquad[\lambda]=4-d.}
$$
These brackets denote <mass dimensions>. The cubic <coupling> is dimensionless at $d=6$, whereas the quartic <coupling> is dimensionless at $d=4$. Hence there is \b[no single dimension] in which both nonzero <couplings> are dimensionless. For example, at $d=4$ the cubic <coupling> still has <mass dimension> one.<Quantum Field Theory by David Tong>[Section 3.1, dimensional analysis of scalar interactions]{ref}
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