**Given Information:**
- The relationship between x and y is given by the equation 3x + 4y = 20.
- The quartile deviation of x is 12.

**Quartile Deviation:**
The quartile deviation measures the spread or dispersion of a set of data. It is calculated as the difference between the upper quartile (Q3) and the lower quartile (Q1).

**Finding the Quartiles:**
To find the quartiles of a set of data, we need to arrange the data in ascending order and then divide it into four equal parts.

**Solving for x:**
Let's solve the equation 3x + 4y = 20 for x.

3x + 4y = 20
3x = 20 - 4y
x = (20 - 4y)/3

**Calculating Quartiles for x:**
Since the quartile deviation of x is given as 12, we can calculate the quartiles using the formula: Q3 - Q1 = 2 * quartile deviation.

Q1 = x - quartile deviation
Q3 = x + quartile deviation

Substituting the value of quartile deviation as 12, we get:

Q1 = x - 12
Q3 = x + 12

**Substituting the Value of x:**
Substituting the value of x in terms of y in the quartile formulas:

Q1 = (20 - 4y)/3 - 12
Q3 = (20 - 4y)/3 + 12

**Calculating the Quartile Deviation for y:**
The quartile deviation for y can be calculated as the difference between the upper quartile (Q3) and the lower quartile (Q1) for y.

Quartile Deviation for y = Q3 - Q1

Substituting the values of Q1 and Q3:

Quartile Deviation for y = [(20 - 4y)/3 + 12] - [(20 - 4y)/3 - 12]
= [(20 - 4y)/3 + 12 - 20 + 4y)/3 + 12
= (4y + 36)/3

Simplifying further:

Quartile Deviation for y = (4y + 36)/3

**Final Answer:**
Therefore, the quartile deviation of y is (4y + 36)/3.

Y=ax+b

Equation => 3x+4y=20

4y=20-3x

y=20-3x/4

y=20/4 - 3/4x

y= 5 - 3/4 x

a=-3/4. b= 5

Qd(x) = 12

Qd(y) = |-3/4| × Qd(x)

Qd(y) = |-3/4| × 12

Qd(y) = 9

Option D is correct