$\begin{array}{rcl} & & \mathrm{Shama} \mathrm{spends} \mathrm{half} \mathrm{of} \mathrm{her} \mathrm{day} \mathrm{sleeping} \mathrm{and} \mathrm{half} \mathrm{of} \mathrm{remaining} \mathrm{day} \mathrm{studying}.\mathrm{In} \mathrm{the} \mathrm{remaining}\\ & & \mathrm{time} \mathrm{she} \mathrm{decides} \mathrm{to} \mathrm{play} \mathrm{chess}.\mathrm{How} \mathrm{many} \mathrm{hours} \mathrm{did} \mathrm{she} \mathrm{played} \mathrm{chess}?\end{array}$

$\begin{array}{rcl} & & \mathrm{Given}:\\ & =& >\mathrm{Time} \mathrm{spent} \mathrm{in} \mathrm{sleeping} =\frac{ 1}{2}\mathrm{day}, \mathrm{time} \mathrm{spent} \mathrm{in} \mathrm{studying}=\frac{1}{2} \mathrm{of} \mathrm{remaining} \mathrm{hours}.\\ & & \mathrm{To} \mathrm{calculate}:\\ & & \mathrm{Time} \mathrm{spent} \mathrm{playing} \mathrm{chess}.\\ & & \mathrm{Calculations}:\\ & =& >\mathrm{Total} \mathrm{hours} \mathrm{in} \mathrm{a} \mathrm{day} = 24 \mathrm{hrs}\\ & =& >\mathrm{Time} \mathrm{spent} \mathrm{sleeping} =\frac{1}{2}\times 24 = 12 \mathrm{hrs}.\\ & =& >\mathrm{Time} \mathrm{spent} \mathrm{studying} = \left(24-12\right)\times \frac{1}{2}=6 \mathrm{hrs}.\\ & =& >\mathrm{Time} \mathrm{spent} \mathrm{in} \mathrm{playing} \mathrm{chess} = 24-12-6=6 \mathrm{hrs}.\\ & & \mathrm{Hence} \mathrm{option} \mathrm{D} \mathrm{is} \mathrm{correct}.\end{array}$