To solve for the volume of the entire object composed of a hemisphere and a cone, we start with the information given:
- The height of the cone (h) is equal to the diameter of the hemisphere (d).
- The volume of the cone is given as 12 m³.
Next, we use the formula for the volume of a cone:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]
Given that \( h = d = 2r \) (because the diameter \( d = 2r \)), we can express the volume of the cone in terms of the radius:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 (2r) = \frac{2}{3} \pi r^3 \]
We know that this volume equals 12 m³:
\[ \frac{2}{3} \pi r^3 = 12 \]
To solve for \( r \), we can multiply both sides by \(\frac{3}{2}\):
\[ \pi r^3 = 18 \]
Then, divide by \( \pi \):
\[ r^3 = \frac{18}{\pi} \]
Now we can find the volume of the hemisphere. The volume of a hemisphere is given by:
\[ V_{\text{hemisphere}} = \frac{2}{3} \pi r^3 \]
Using the value we found for \( r^3 \):
\[ V_{\text{hemisphere}} = \frac{2}{3} \pi \left( \frac{18}{\pi} \right) = \frac{2}{3} \cdot 18 = 12 \text{ m}^3 \]
Now, we can find the total volume of the object (hemisphere + cone):
\[ V_{\text{total}} = V_{\text{hemisphere}} + V_{\text{cone}} = 12 \text{ m}^3 + 12 \text{ m}^3 = 24 \text{ m}^3 \]
Thus, the volume of the whole object is:
\[ \boxed{24 \text{ m}^3} \]