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I will attempt some pictures.
First draw the world lines of the Earth and Mars with the events in question. This should look like two vertical lines with marks at exactly the same level since the events happen at the same time in the Earth frame of reference.
Second draw the world line of the ship traveling from Earth toward Mars. That should be a line inclining somewhat to the right as shown (I hope) below.
Now draw the lines of constant time as seen by the ship. Remember they would be horizontal if the ship were not moving. Since the ship's world line is rotated clockwise, the lines of constant time rotate counterclockwise and you get a picture like this:
Notice that the black line that represents events happening the same time as the event on Mars crosses the ship's world-line BEFORE the black line that represents events happening at the same time as the event on Earth.
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