Explanation

Let the number be x.

Two-third of the number is (2/3)x.

The problem states that multiplying the number by two-third of itself gives 864, so we can set up the equation: x × (2/3)x = 864.

Simplifying the equation, we get: (2/3)x² = 864.

Multiplying both sides by 3/2, we get: x² = 864 × (3/2) = 1296.

Taking the square root of both sides, we get: x = √1296 = 36.

So, the correct answer is: 36