Solution:

Given equations of regression lines:
1) 3X + 6Y + 7 = 0
2) 5X + 3Y + 8 = 0

We know that the equation of a regression line is given by:
Y = aX + b
where a is the slope and b is the intercept of the regression line.

To find the slope and intercept of the regression lines, we need to rearrange the given equations in the form Y = aX + b.

Re-arranging equation 1:
6Y = -3X - 7
Y = (-3/6)X - (7/6)
Y = (-1/2)X - (7/6)

Comparing this equation with Y = aX + b, we get:
a1 = -1/2 (slope)
b1 = -7/6 (intercept)

Re-arranging equation 2:
3Y = -5X - 8
Y = (-5/3)X - (8/3)

Comparing this equation with Y = aX + b, we get:
a2 = -5/3 (slope)
b2 = -8/3 (intercept)

Now, let's calculate the standard deviation of X (SD{x}).

We are given that SD{x} = 4.

Using the formula for standard deviation:

SD{x} = sqrt[(∑(X - mean(X))^2) / n]

Since we have only one value of X, which is 1, the mean of X is also 1.

4 = sqrt[(1 - 1)^2 / 1]
4 = sqrt[0]
4 = 0

This implies that there is an error in the given value of SD{x}. It cannot be zero.

Since we cannot calculate the standard deviation of X, we cannot determine the standard deviation of Y either.

Therefore, the correct answer is d) none of these.

Please note that the given values seem to be inconsistent and might have errors.