A conducting circular loop is placed in X - Y plane in presence of...

By the faraday's law in electromagnetic induction

${ε}_{ind} = - \dfrac{d ϕ}{d t} = - \dfrac{d \left(\overset{\to}{B} \cdot \overset{\to}{A}\right)}{d t}$

Magnetic flux is $ϕ = \overset{\to}{B} \cdot \overset{\to}{A}$= \left(3{t}^{3}\overset{^}{j} + 3{t}^{2}\overset{^}{k}\right) \cdot \left(\pi{\left(1\right)}^{2}\overset{^}{k}\right)

So, $ϕ = 3{t}^{2}\pi$

Now, induced emf is ${ε}_{ind} = \left|\dfrac{d ϕ}{d t}\right| = 6t\pi$

At $t = 2, {ε}_{ind} = 6\left(2\right)\pi = 12\piV$.

Thus, the value of $n = 12$.