The general form of the equation of a circle with its center at (a, b) is
(x - a)² + (y - b)² = (radius)² .
So if the center of your circle is at (-2, 1)
we know that the left side of the equation is
(x + 2)² + (y - 1)² = . . .
For the right side of the equation, we need to know the circle's radius.
Well, you said that the point (-4, 1) is on the circle.
How far is that point from the center at (-2, 1) ?
It looks to me like the distance between (-2, 1) and (-4, 1) is 2 units.
So the radius of the circle is 2 , and the full equation is ...
(x + 2)² + (y - 1)² = 4 .