The centroid (intersection of medians) of the triangle $ ABC $ is point:
$$\left(2,~3\right) $$The centroid of a triangle is given by:
$$ O = \left( \frac{A_x + B_x + C_x}{3} ~ , ~ \frac{A_y + B_y + C_y}{3} \right) $$where $ A_x $ and $ A_y $ are $ x $ and $ y $ coordinates of the point $ A $ , $ B_x $ and $ B_y $ are $ x $ and $ y $ coordinates of the point $ B $ etc..
In this example we have : $ A_x = 4 $ , $ A_y = 0 $ , $ B_x = 2 $ , $ B_y = 9 $ , $ C_x = 0 $ and $ C_y = 0 $ .
When we insert these values into the formula, we obtain the given result.