**Given:**
- Length of the first capillary tube = l
- Radius of the first capillary tube = r
- Rate of flow of water through the first capillary tube = V

**To find:**
Rate of flow of water through the second capillary tube of length 2l and radius 2r for the same pressure difference.

**Assumptions:**
- The flow of water is laminar.
- The viscosity of water remains constant.

**Explanation:**
The rate of flow of a fluid through a capillary tube depends on various factors, including the length, radius, and pressure difference across the tube. According to Poiseuille's law, the rate of flow (V) is directly proportional to the pressure difference (ΔP) and the fourth power of the radius (r), and inversely proportional to the length (l) and viscosity (η) of the fluid.

Mathematically, the Poiseuille's law equation is given by:
V = (πΔP r^4)/(8ηl)

We are given that the pressure difference across both capillary tubes is the same. Therefore, ΔP remains constant.

**Comparison of the two capillary tubes:**

1. Length:
- The length of the first capillary tube is l.
- The length of the second capillary tube is 2l.
- As per Poiseuille's law, the rate of flow is inversely proportional to the length of the tube. Therefore, the rate of flow through the second capillary tube will be half of the rate of flow through the first capillary tube.

2. Radius:
- The radius of the first capillary tube is r.
- The radius of the second capillary tube is 2r.
- As per Poiseuille's law, the rate of flow is directly proportional to the fourth power of the radius of the tube. Therefore, the rate of flow through the second capillary tube will be 16 times the rate of flow through the first capillary tube (2^4 = 16).

Combining the effects of length and radius, we can conclude that the rate of flow through the second capillary tube will be:
16 times the rate of flow through the first capillary tube due to the change in radius, and
half the rate of flow through the first capillary tube due to the change in length.

Therefore, the overall rate of flow through the second capillary tube will be 16 * 1/2 = 8 times the rate of flow through the first capillary tube.

Hence, the correct answer is option C: 8V.