**To find the value of p for which the pair of linear equations has only one solution, we need to solve the equations and find the conditions under which the solution is unique.**

1. **Given Equations:**
The given pair of linear equations is:
p/x + 3/y = 8 ...(1)
4/x - 12y = 56 ...(2)

2. **Conditions for Unique Solution:**
In order for the pair of linear equations to have a unique solution, the determinant of the coefficient matrix should be non-zero. This condition is known as the consistency condition.

3. **Determinant of Coefficient Matrix:**
The coefficient matrix for the given equations is:
| 1/x 1/y |
| 4 -12 |

The determinant of this matrix is:
| 1/x 1/y |
| 4 -12 | = (1/x)(-12) - (1/y)(4) = -12/x - 4/y

4. **Condition for Unique Solution:**
For the pair of linear equations to have a unique solution, the determinant of the coefficient matrix should be non-zero. Therefore, we can set the determinant equal to zero and solve for p.

-12/x - 4/y = 0
-12/x = 4/y
-12y = 4x
y = -1/3x

Substituting this value of y in equation (1):
p/x + 3/(-1/3x) = 8
p/x - 9/x = 8
(p - 9)/x = 8

As the left side of the equation depends on x and the right side is a constant, for a unique solution, the left side should also be a constant. Therefore, the numerator (p - 9) should be equal to zero.

p - 9 = 0
p = 9

5. **Conclusion:**
Therefore, for the pair of linear equations p/x + 3/y = 8 and 4/x - 12y = 56 to have only one solution, the value of p should be 9.