We are given the ratio of daisies to lilies to daffodils as $4h:9:2h$. We need to find the fraction of the flowers in the bouquet that are lilies.

1. Problem Description

We are given the ratio of daisies to lilies to daffodils as $4h:9:2h$. We need to find the fraction of the flowers in the bouquet that are lilies.

2. Solution Steps

First, we need to find the total number of flowers in the bouquet. We do this by adding up the parts of the ratio.

Total flowers = daisies + lilies + daffodils.

Total flowers $= 4h + 9 + 2h$

Total flowers $= 6h + 9$

Next, we want to find the fraction of lilies in the bouquet. This is the number of lilies divided by the total number of flowers.

Fraction of lilies = $\frac{\text{Number of lilies}}{\text{Total number of flowers}}$

Fraction of lilies $= \frac{9}{6h + 9}$

We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is

3. Fraction of lilies $= \frac{9 \div 3}{(6h + 9) \div 3}$

Fraction of lilies $= \frac{3}{2h + 3}$

3. Final Answer

The fraction of the flowers in the bouquet that are lilies is $\frac{3}{2h+3}$.