To find the product of two numbers given their ratio and H.C.F, we can follow these steps:

Understanding the Ratio
- The ratio of the two numbers is 3:4.
- This means if we denote the two numbers as 3x and 4x, where x is a common multiplier.

Using the H.C.F
- The H.C.F (Highest Common Factor) of the two numbers is given as 6.
- Since the H.C.F is the common factor, we can express both numbers in terms of their H.C.F.

Finding the Values of the Numbers
- From the ratio, we know:
- First number = 3x
- Second number = 4x
- Since the H.C.F is 6, we can set the values:
- 3x = 6 (for the first number)
- 4x = 6 (for the second number)
- Solving for x:
- From 3x = 6, we find x = 6/3 = 2.

Calculating the Numbers
- Now, substituting x back into the expressions for the numbers:
- First number = 3x = 3 * 2 = 6
- Second number = 4x = 4 * 2 = 8

Finding the Product
- The product of the two numbers is:
- Product = First number × Second number
- Product = 6 × 8 = 48

Conclusion
- Therefore, the product of the two numbers is **48**. This method highlights the relationship between ratios, H.C.F, and multiplication effectively.