Let v be the speed of the projectile, be it a dart or a marble. It covers a horizontal distance x with height y at time t according to
x = v t
y = 1.5 m - 1/2 g t²
where g = 9.80 m/s² is the magnitude of the acceleration due to gravity.
The projectile lands 4 m from the table, so it hits the ground at time t such that
4 m = v t ==> t = (4 m) / v
It's on the ground, so that y = 0 at this time. Substitute this into the height equation and solve for v :
0 = 1.5 m - 1/2 g ((4 m) / v)²
v² = (g (16 m²)) / (3.0 m)
v ≈ 7.23 m/s