OK, let's solve the equation step by step:
First, the equation is: $$\sqrt[3]{4x+8} = 1.5$$
To eliminate the cube root, we need to raise both sides of the equation to the power of 3:
$$(\sqrt[3]{4x+8})^3 = (1.5)^3$$
This simplifies to:
$$4x+8 = 3.375$$
Now, subtract 8 from both sides:
$$4x = 3.375 - 8$$
$$4x = -4.625$$
Finally, divide both sides by 4:
$$x = \frac{-4.625}{4}$$
$$x = -1.15625$$
So the solution is:
Answer: -1.15625