This is a difficult question! You will need a solid grasp of dot diagrams and position-time graphs in order to be successful on this question. There are three dot diagrams in the upper left of the graphic. Notice that the three objects have different speeds as denoted by the spacing between adjacent dots. Also notice that one of the three objects is moving to the right and the other two to the left; this is shown by the arrow. The rightward-moving object has a positive velocity; it will have to be matched to one of the three graphs that show a positive velocity. The other two leftward-moving objects will have to be matched to two of the three lines that show a leftward velocity.
On the dot diagram, the faster-moving object moves the greatest distance in the time between dots. So the object with the greatest speed is the one with the greatest spacing between dots. And the slowest-moving object (smallest speed) has the smallest spacing between dots. Take a moment to identify the order of speeds for the three objects - smallest, middlest, and greatest - based on the dot diagrams. Then you will be closer to being able to make a match of each dot diagram to one of the six lines on the graph.
There are six lines on the position-time graph to choose from. Three of the choices are lines with positive slope; these represent a positive velocity. You will have to match one of these lines to the one object that is moving to the right (i.e., have a positive velocity). And three of the lines have a negative slope; match two of these to the two objects that have a negative velocity (i.e., a leftward velocity). You might take a moment to make a note of the possibilities for A, B, and C. Then you will have some final narrowing down to do. Read on ...
Every upward-sloped line has a different slope. And for each upward sloped line, there is a corresponding downward-sloped line that has the same amount of slope to it ... but only downward. So there are two slow lines - one for rightward motion (upward or positive slope) and one for downward motion (downward or negative slope). Similarly, there are two fast lines - one for each direction of motion. And there are two intermediate speed lines. The two lines that slope the most - either sloping down or up - correspond to the fastest-moving objects. And the two lines that slope the least (i.e., are flattest) correspond to the slowest-moving objects. Now if you've taken the time to rank the three objects according to speed and if you can identify which two objects are moving rightward and which one is moving leftward, then you are ready to make the final match.