In the given questions, two quantities are given. One as Quantity-I and another is Quantity-II. You have to determine relationship between these two quantities and choose the appropriate options as given below:
Quantities:
I. Values of x, if `6x^2-23x+20=0`
II. Values of y, if `3y^2-10y+8=0`

Options

A. Quantity- I `gt` Quantity-II
B. Quantity- I `lt` Quantity-II
C. Quantity- I `le` Quantity-II
D. relation between X and Y cannot be determined

Answer

To solve the problem, we need to find the values of \( x \) and \( y \) from the given quadratic equations and then compare them.

### Step 1: Solve for \( x \) in the equation \( 6x^2 - 23x + 20 = 0 \)

We will use the factorization method.

1. **Identify coefficients**:
- \( a = 6 \)
- \( b = -23 \)
- \( c = 20 \)

2. **Calculate the product \( ac \)**:
\[ ac = 6 \times 20 = 120 \]

3. **Find two numbers that multiply to \( ac \) (120) and add to \( b \) (-23)**:
- The numbers are -15 and -8 because:
\[ -15 \times -8 = 120 \quad \text{and} \quad -15 + (-8) = -23 \]

4. **Rewrite the equation**:
\[ 6x^2 - 15x - 8x + 20 = 0 \]

5. **Group the terms**:
\[ (6x^2 - 15x) + (-8x + 20) = 0 \]

6. **Factor by grouping**:
\[ 3x(2x - 5) - 4(2x - 5) = 0 \]
\[ (3x - 4)(2x - 5) = 0 \]

7. **Set each factor to zero**:
\[ 3x - 4 = 0 \quad \Rightarrow \quad x = \frac{4}{3} \]
\[ 2x - 5 = 0 \quad \Rightarrow \quad x = \frac{5}{2} \]

### Step 2: Solve for \( y \) in the equation \( 3y^2 - 10y + 8 = 0 \)

1. **Identify coefficients**:
- \( a = 3 \)
- \( b = -10 \)
- \( c = 8 \)

2. **Calculate the product \( ac \)**:
\[ ac = 3 \times 8 = 24 \]

3. **Find two numbers that multiply to \( ac \) (24) and add to \( b \) (-10)**:
- The numbers are -6 and -4 because:
\[ -6 \times -4 = 24 \quad \text{and} \quad -6 + (-4) = -10 \]

4. **Rewrite the equation**:
\[ 3y^2 - 6y - 4y + 8 = 0 \]

5. **Group the terms**:
\[ (3y^2 - 6y) + (-4y + 8) = 0 \]

6. **Factor by grouping**:
\[ 3y(y - 2) - 4(y - 2) = 0 \]
\[ (3y - 4)(y - 2) = 0 \]

7. **Set each factor to zero**:
\[ 3y - 4 = 0 \quad \Rightarrow \quad y = \frac{4}{3} \]
\[ y - 2 = 0 \quad \Rightarrow \quad y = 2 \]

### Step 3: Compare the values of \( x \) and \( y \)

- The values of \( x \) are \( \frac{4}{3} \) and \( \frac{5}{2} \).
- The values of \( y \) are \( \frac{4}{3} \) and \( 2 \).

#### Comparison:
1. When \( x = \frac{4}{3} \), \( y = \frac{4}{3} \) → \( x = y \)
2. When \( x = \frac{4}{3} \), \( y = 2 \) → \( x < y \)
3. When \( x = \frac{5}{2} \), \( y = \frac{4}{3} \) → \( x > y \)
4. When \( x = \frac{5}{2} \), \( y = 2 \) → \( x > y \)

### Conclusion:
The relationship between \( x \) and \( y \) cannot be determined definitively since \( x \) can be both less than and greater than \( y \) depending on the specific values chosen.

### Final Answer:
The correct option is **(D) The relationship cannot be determined**.