I would answer this by using the quadratic formula to figure out which equation only has one solution. quadratic formula: (-b(+or-)√(b^2-(4ac)))/2a. You find that the equation 4x²+12x+9=0 only has the root of x=-1.5.
Since the solution is where the parabola crosses the x-axis, you can also figure out which equation has only one solution by whether or not the axis of symmetry lands is a solution or not. If the axis of symmetry is a solution, the function only has one solution (that being the vertex). If the axis of symmetry is not a solution, the function has to have either two or no roots. You can find the axis of symmetry by using the equation x=-b/2a. Using that equation you can find that the equation 4x²+12x+9 has the axis of symmetry being at x=-1.5 which means that the vertex is (-1.5,0). Since the equation 4x²+12x+9 has its vertex at (-1.5,0) and the vertex is the lowest or highest point of the function, that function only has one x-intercept meaning it only has 1 solution.
I hope this helps. Let me know in the comments if anything is unclear.
