LW = Longwave radiation (i.e. Infrared radiation)
SW = Shortwave radiation (i.e. Visible + Ultraviolet light)
For the left part of the diagram, it shows that the 30% of the total incoming energy (mostly delivered as shortwave radiation) gets reflected by clouds and the Earth's surface. Therefore, 70% is the total absorbed by the planet (45% of it is absorbed by the Surface and 25% by the atmosphere).
The red line refers to the fact that given that Earth energy budget is assumed to be in balance, meaning that the same amount of energy that goes IN the system (as shortwave radiation) must go OUT the system, in the form of longwave radiation, that is the main kind of radiation the Earth emits given its temperature (see Wien's law). This energy balance assumption is a good one, because even if you think that more energy gets IN than OUT, that would lead Earth's temperature to increase, increasing then the amount of emitted energy (according to Stefan–Boltzmann law), until it reaches a point where the outgoing radiation released equals the amount received energy from the Sun. Therefore, establishing the energy balance.
Due to this balance, the right part of the diagram shows that the same 70% of the energy must be emitted back to space as longwave radiation (the same amount that was absorbed), and for that to be true, it is asking you what would be the required amount of energy that the atmosphere must emit towards Earth as LW radiation to keep the system in balance. Or at least that's my interpretation of the question marks in the absence of further information.