If the equivalent capacitance between points A and B of the combination of capacitors shown in figure, is 6C, the capacitor $C^1$ is

The capacitors $2C$, $3C$, and $4C$ are connected in parallel. Their equivalent capacitance is:
$C_p = 2C + 3C + 4C = 9C$

This combination is in series with $C^1$. The total equivalent capacitance between A and B is $6C$.

Using the formula for series combination:
$\dfrac{1}{C_{eq}} = \dfrac{1}{C_p} + \dfrac{1}{C^1}$

$\dfrac{1}{6C} = \dfrac{1}{9C} + \dfrac{1}{C^1}$

$\dfrac{1}{C^1} = \dfrac{1}{6C} - \dfrac{1}{9C}$

$\dfrac{1}{C^1} = \dfrac{3 - 2}{18C} = \dfrac{1}{18C}$

$C^1 = 18C$

Answer: $18C$