Identify the relevant component of magnetic field

The circular loop lies in the $X$-$Y$ plane, so its area vector is along the $\hat{k}$ direction.

Given, $\vec B = 3t^3\,\hat{j} + 3t^2\,\hat{k}$

Only the component perpendicular to the loop contributes to magnetic flux, i.e. the $\hat{k}$ component: $B_\perp = 3t^2$

Area of the circular loop

Radius $r=1\text{ m}$, so $A = \pi r^2 = \pi$

Magnetic flux through the loop

$\Phi = B_\perp A = (3t^2)(\pi) = 3\pi t^2$

Induced emf using Faraday's law

$\mathcal E = \left| -\frac{d\Phi}{dt} \right| = \left|\frac{d}{dt}(3\pi t^2)\right| = 6\pi t$

At $t=2\text{ s}$

$\mathcal E = 6\pi(2) = 12\pi\text{ V}$

Comparing with $n\pi\text{ V}$, $n=12$

Comparison with stored answer

Stored correct answer = $12$

This matches our derived answer.