To observe the solar flare detected by the satellite at 10:00 P.M. from Earth, you should look at the Sun at 10:08 P.M. Earth time, which accounts for the 8-minute light travel time from the Sun to Earth.
The question pertains to the observation of a solar flare and when it would be visible from Earth, given the flare was detected by a satellite that orbits close to the Sun. The Sun is approximately 8 light minutes away from Earth. Therefore, if a solar flare was detected by a satellite at 10:00 P.M. (satellite time), the light from this flare will take approximately 8 minutes to travel from the Sun to Earth. Consequently, to observe this solar flare from your backyard, you should look at the Sun at about 10:08 P.M. Earth time, assuming that the satellite's clock is synchronized with Earth time and not accounting for the time it takes for the light to travel from the flare to the satellite.