Given the four lines with the equations
`x+2y-3=0`, `3x+4y-7=0`,
`2x+3y-4=0`, `4x+5y-6=0`, then

Options

A. they are all concurrent
B. they are all sides of a quadrilateral
C. only three lines are concurrent
D. None of the above

Answer

To determine whether the given four lines are concurrent, we will analyze the equations of the lines:

1. **Equations of the Lines**:
- Line 1: \( x + 2y - 3 = 0 \) (let's call this \( L_1 \))
- Line 2: \( 3x + 4y - 7 = 0 \) (let's call this \( L_2 \))
- Line 3: \( 2x + 3y - 4 = 0 \) (let's call this \( L_3 \))
- Line 4: \( 4x + 5y - 6 = 0 \) (let's call this \( L_4 \))

2. **Finding the Intersection of Lines**:
We will check if the lines are concurrent by finding the intersection point of any three lines and checking if the fourth line passes through that point.

3. **Finding Intersection of \( L_3 \) and \( L_4 \)**:
We will eliminate \( y \) by manipulating the equations of \( L_3 \) and \( L_4 \).

- From \( L_3 \):
\[ 2x + 3y - 4 = 0 \implies 3y = 4 - 2x \implies y = \frac{4 - 2x}{3} \]

- Substitute \( y \) in \( L_4 \):
\[ 4x + 5\left(\frac{4 - 2x}{3}\right) - 6 = 0 \]
Multiply through by 3 to eliminate the fraction:
\[ 12x + 5(4 - 2x) - 18 = 0 \]
Simplifying:
\[ 12x + 20 - 10x - 18 = 0 \implies 2x + 2 = 0 \implies 2x = -2 \implies x = -1 \]

- Substitute \( x = -1 \) back into \( L_3 \) to find \( y \):
\[ 2(-1) + 3y - 4 = 0 \implies -2 + 3y - 4 = 0 \implies 3y = 6 \implies y = 2 \]

- Thus, the intersection point of \( L_3 \) and \( L_4 \) is \( (-1, 2) \).

4. **Checking if \( (-1, 2) \) lies on \( L_1 \)**:
Substitute \( (-1, 2) \) into \( L_1 \):
\[ -1 + 2(2) - 3 = -1 + 4 - 3 = 0 \quad \text{(True)} \]

5. **Checking if \( (-1, 2) \) lies on \( L_2 \)**:
Substitute \( (-1, 2) \) into \( L_2 \):
\[ 3(-1) + 4(2) - 7 = -3 + 8 - 7 = -2 \quad \text{(False)} \]

6. **Conclusion**:
The point \( (-1, 2) \) lies on \( L_1 \), \( L_3 \), and \( L_4 \) but not on \( L_2 \). Therefore, three of the lines are concurrent, while the fourth line does not pass through this point.

### Final Answer:
Only three of the lines are concurrent.