the given equation is in slope intercept form
y=mx+b
y=7/3x+3
m = Slope
b = y-intercept
so we know that the slope of your first line is 7/3 and the y intercept is 3
for two lines to be paralell they have to have the same slope. We can start with that. We know that the equation of the second line must start with
y=7/3x+?
to find another point on the second line you can use rise over run to move from (-3,-3) up 7 and to the right 3 on the graph to
(0,4)
since your x value for this point is 0 that is your y-intercept.
y=7/3x+4
Here is a graph of both lines: