In this question, we are given three liquids with densities of D, 2D, and 3D respectively. We are asked to determine the density of the resulting mixture when equal volumes of these three liquids are mixed.

To solve this problem, we can consider the principle of the conservation of mass. Since equal volumes of each liquid are being mixed, we can assume that the mass of each liquid is equal. Therefore, we can say that the total mass of the mixture is the sum of the masses of the three liquids.

Let`s assume that the volume of each liquid is V. Since the density of a substance is defined as its mass divided by its volume, we can say that the mass of the first liquid is D x V, the mass of the second liquid is (2D) x V, and the mass of the third liquid is (3D) x V.

Adding these masses together, we get the total mass of the mixture as (D x V) + (2D x V) + (3D x V) = 6D x V.

Now, to find the density of the mixture, we divide the total mass by the total volume. Since the volume of each liquid is the same, the total volume is also V. Therefore