Which one of the following is the resistance that must be placed parallel with $15\Omega$ resistances to obtain a combined resistance of $6\Omega$? 

Parallel arrangement: If the ends of two or more resistors are connected in a similar manner on one end, then the resistors are said to be connected in parallel.

$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$

Here, $R_1,R_2,R_3$. are the resistance of the branches of a parallel circuit.

Given data- $R_1=15\Omega \text{ and }{R}_{eq}=6\Omega ,R_2=\text{ ? }$

$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}$

$\frac{1}{6}=\frac{1}{15}+\frac{1}{R_2}\Rightarrow \frac{1}{R_2}=\frac{1}{6}-\frac{1}{15}\Rightarrow \frac{1}{R_2}=\frac{5-2}{30}$

Then,

$\frac{1}{R_2}=\frac{3}{30}=\frac{1}{10}$

Now,

$R_2=10\Omega$