If the value of the first four raw moments is 2, 4, 5 and 6, respectively. then the value of the fourth central moment is: 

Key Points 

The raw moments (or moments about the origin) and the central moments (or moments about the mean) are two different ways of characterizing a probability distribution. The raw moments are calculated at about 0, while the central moments are calculated at about the mean.
The first four raw moments of a distribution, as you specified, are given as 2, 4, 5, and 6 respectively. These tell us about the mean, variance, skewness, and kurtosis of the distribution respectively.
The first raw moment is the mean (µ) of the distribution. So, in this case, the mean is 2.
The second, third, and fourth central moments are given by:

• Second central moment (σ²) = μ₂ - μ₁²
• Third central moment = μ³ - 3μ₁μ² + 2μ₁³
• Fourth central moment = μ⁴ - 4μ¹μ³ + 6μ₁²μ² - 3μ₁⁴

Substitutiong the given information μ₁=2, μ₂=4, μ₃=5, and μ₄=6; 
Now we can substitute these into the formula to find the fourth central moment:
Fourth Central Moment = \(μ_4 - 4μ_1μ_3 + 6μ_1^2μ_2 - 3μ_1^4\) = 6 - 4 × 2 × 5 + 6 × 2²× 4 - 3 × 2⁴ = 6 - 40 + 96 - 48 = 14

Hence, the value of the fourth central moment is 14.