Which of the following resistance must be placed parallel with 15 Ω resistance to obtain an equivalent resistance of 6 Ω? 

When two or more resistances are connected in parallel combination, the equivalent resistance is given by:

$\frac{1}{{\mathrm{R}}_{\mathrm{eq}}}=\frac{1}{{\mathrm{R}}_1}+\frac{1}{{\mathrm{R}}_2}$

We have been given,  R₁ = 15 Ω, and R_eq = 6 Ω

$\frac{1}{6}=\frac{1}{15}+\frac{1}{{\mathrm{R}}_2}$
$\Rightarrow \frac{1}{{\mathrm{R}}_2}=\frac{1}{6}-\frac{1}{15}$
$\Rightarrow \frac{1}{{\mathrm{R}}_2}=\frac{5-2}{30}= \frac{3}{30}$

$\therefore {\mathrm{R}}_2=10\mathrm{\Omega }$

Therefore,  10 Ω resistance must be placed parallel with 15 Ω resistances to obtain an equivalent resistance of 6 Ω.