when small lines appearing on mount of luna (moon) and it joins the fate line, it represents the influence of opposite sex in your life(Influence Line). It also significe the sign of marriage, a happy marriage.
In case the line cuts the line of fate and cross it, show the opposite influence in life.
It may shows obstacle and suffering, because of person came in your life.
As per Cheiro,
If the Influence line should cut through the fate line, and appear on th thumb side of it, the affection will seldom lst as long, or be so happy.