Solution:

Understanding the Problem:

We are given that x and y are related by the equation 2x + 3y + 4 = 0. We are also given that the standard deviation (SD) of x is 6. We need to find the SD of y.

Methodology:

To find the SD of y, we first need to find the relationship between x and y. We can rearrange the given equation as follows:

2x + 3y + 4 = 0
3y = -2x - 4
y = (-2/3)x - (4/3)

This shows us that y is a linear function of x with a slope of -2/3 and an intercept of -4/3. This means that as x increases, y decreases and vice versa.

We can use this relationship to find the SD of y using the following formula:

SD(y) = |b| * SD(x)

where b is the slope of the linear relationship between x and y.

Calculations:

From the equation above, we can see that the slope of the linear relationship between x and y is -2/3. Therefore,

SD(y) = |-2/3| * SD(x)
SD(y) = 2/3 * 6
SD(y) = 4

Therefore, the SD of y is 4.

Conclusion:

In conclusion, if x and y are related by the equation 2x + 3y + 4 = 0 and the SD of x is 6, then the SD of y is 4. This is because y is a linear function of x with a slope of -2/3, which means that the SD of y is proportional to the SD of x with a factor of |-2/3|.