Question

The Moon phase in which the amount of lighted
surface seen on earth increases.

Answer 1

The Waxing Crescent phase. It occurs when the western edge of the Moon is lit but most of the surface visible from Earth is dark. The amount of illumination visible is growing from day to day during this phase which is what is meant by "waxing."

Answer 2

a full moon is the moon phase in which the amount of lighted surface seen on earth increases