Parallel lines have the same slope, so the slope of the equation you are looking for would be 2/3.
The only information missing now is the y-intercept. The slope of the line you are looking for is 2/3: slope represents rise/run or another way to say it is for every 3 points the line moves to the right, it must move 2 points upward. You also know that the line passes through point (6,7), remember points are represented as (x,y), so for this particular point x=6 and y=7. You are looking for the Y-intercept, the Y-intercept is the point where the line crosses the y-axis which by definition is where x=0, so you want to move your (6,7) point to (0,y) in order to get the y-intercept. The key to solving the problem is to notice that the slope moves by 3 points at a time on the x-axis and at the same time the point on the line given to you in the question is 6 points on the x-axis; 3 divides into 6 evenly! If you reduce the point given to you in the question by 2 groups of 3, then it will be at zero, which is the y-intercept. Since you reduced the x-axis by two groups, you need to reduce the y-axis by two groups, and since each group of the y-axis moves by two, you reduce the y point by four. the y point started out as 7, so now it is 3.
your answer is y=2/3x+3