Find the least value of `3x+4y` for positive values of x and y, dubject to the condition `x^(2)y^(3)=6`.

Explanation

To find the least value of \(3x + 4y\) for positive values of \(x\) and \(y\) subject to the constraint \(x^2 y^3 = 6\), we can use the method of Lagrange multipliers or the AM-GM inequality. Here, we will use the AM-GM inequality for simplicity.

### Step-by-Step Solution:

1. **Identify the variables and the constraint**:
We need to minimize \(3x + 4y\) subject to the constraint \(x^2 y^3 = 6\).

2. **Express the function to minimize**:
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