Question

what can you tell about the motion of an object whose distance Time graph is a straight line parallel to X-axis

Answer 1

Thank you for asking this question. This a really interesting but an easy question.
In a distance time graph distance is usually on the y axis and time is always on the x axis. If its a horizontal line parallel to x axis this means that the time is going on but no distance is being covered. 
So basically it is at rest.
I hope this answer can help you in some manner.

Answer 2

the motion of the body is 0 or the body is at rest whose distance time graph is a straight line parallel to x-axis. since, the graph shows the body is only moving in time but no change in its distance or no change in body 's position. so body is at rest