Drawing the picture will for sure help. Draw the circle (you can get its radius and center from the equation- let us know if you need help with that).
Then draw a line from the center of the circle to that point on it (-4,2). You will need the slope of this line to figure out the slope of the tangent line.
The "tangent line" just touches the circle at that one point (-4,2). Picture like putting a stick on the side of the circle. As said above, this tangent line will actually be perpendicular (at a 90 degree angle to) the other line you drew from the center to the point. Hopefully you know how the slopes of perpendicular lines are related!!