Knowing about thermodynamical laws and conservation of energy would be enough to find correct answer.
The total radiated power in all directions
Total radiated power wouldn't be
total if excluding some directions, adding "all directions" once more can cost unclear further assumptions.
peak power is 8dB higher in one direction
Given relative directive gain in one direction is 8 dBi. It is not a power gain expressed in dB. Omitting (i) is no good idea. It is not either possible to assume a power ratio ("db higher in one direction") relative any other directions as we not have information about these other directions, or better expressed as a radiation sphere surface area, where size of current 8dBi area compared to any else part of the sphere area is unknown (gain&area).
As the antenna is assumed lossless do it not consume any power. If feed by 1 Watt will it also radiate same amount of power.
Amount of radiated power will not increase if concentrated in a narrow beam.
If power increases due to a narrower antenna radiation pattern would result in a system delivering more power then it is feed with -> Nobel-prize for the one that succeeds.
Compare with headlight of a car. A reflector add directive gain and can increase light intensity at a certain distance and direction, at cost of radiation intensity in other directions. Amount of radiated power will however remain constant with or without reflector.
Maybe did original study question include other questions such as difference between TRP and EIRP, which would make given answer alternatives a bit more educational.