The correct answer is OLR is highest during their summer and lowest during their winter.
The other answer choices are incorrect. There is no general east to west increase in OLR over the course of 12 months. OLR is highest at the summer solstice, not the vernal equinox. And there is no general west to east increase in OLR over the course of 6 months.
The reason why OLR is highest during summer and lowest during winter is because the Earth's surface is warmer in the summer, which leads to increased thermal radiation. Cloud cover also plays a role, as clouds reflect incoming solar radiation and block outgoing thermal radiation. In the winter, there is more cloud cover in the Northern Hemisphere, which leads to lower OLR values.
The same pattern is observed in the Southern Hemisphere, with OLR being highest in the summer and lowest in the winter.