Notice that the equation given:
4 x + 6 = x + 3
has been represented on the plane by graphing the lines:
y = 4 x + 6, and y = x + 3
and looked for the point at which they intersect.
That point is marked in blue, and we can read its coordinates:
x = -1 and y = 2
so the value for x is -1.
Then we say that the equation 4 x + 6 = x + 3 has for solution x = -1.