Let's break down the problem step-by-step to find out how many boys can swim.

1. Total number of children: $43$

2. Number of children who cannot swim: $6$

3. Number of children who can swim: $43 - 6 = 37$

4. Let $B$ be the total number of boys.

5. Number of boys who can swim: $\frac{15}{17} \times B$

6. Number of boys who cannot swim: $\frac{2}{9} \times B$

We know that the total number of children who cannot swim is 6. Since $\frac{2}{9}$ of the boys cannot swim, we can set up the following equation: $\frac{2}{9} \times B = 6$

Solving for $B$: $B = 6 \times \frac{9}{2}$ $B = 27$

So, there are 27 boys in total.

7. Number of boys who can swim: $\frac{15}{17} \times 27$

Calculating this: $\frac{15}{17} \times 27 = \frac{15 \times 27}{17} = \frac{405}{17} \approx 23.82 \approx 24$

Therefore, the number of boys who can swim is approximately 24.

Would you like more details or have any questions?

Here are 5 numbered questions for you to ask:

1. Can you explain the step-by-step solution for solving algebraic equations?
2. How do you solve quadratic equations?
3. What is the process for solving systems of linear equations?
4. Can you explain the properties of logarithms and how to use them?
5. How do you find the derivative of a function using calculus?

Tip: Always double-check your calculations and ensure each step logically follows from the previous one to avoid errors in complex problems.