Two rectangular blocks, having identical dimensions, can be...

In the first combination, the 2 blocks are having thermal conductivity $2K$ and $2K$ respectively are in series combination.

Therefore the Keq will be $\dfrac{1}{K} + \dfrac{1}{2K}$

and the Keq in case of parallel combination is 3K

$\text{Heat transferred} = \text{Rate} \times \text{time. }$
$∴ {\text{Rate}}_{1} \times {\text{time}}_{1} = {\text{Rate}}_{2} \times {\text{time}}_{2} .$
$\dfrac{\Delta \text{T} \times 9}{\dfrac{\text{L}}{\text{KA}} + \dfrac{\text{L}}{2 \text{KA}}} = \dfrac{\text{\Delta} \text{T} \times \text{t}}{\dfrac{L}{\text{3KA}}}$
$⇒ \text{t} = 2$