To solve for \(x\) and \(y\) in the given triangles, we can use the Pythagorean theorem. Here’s how you can solve each part:

**c) Triangle \(ABC\):**

Given:
- \(AB = x\)
- \(AC = 14\)
- \(BC = 16\)

Using Pythagorean theorem in \(\triangle ABC\):
\[
x^2 + y^2 = 14^2
\]
Given that \(BC = x + y = 16\), we can express \(y\) as \(y = 16 - x\).

**d) Triangle \(DEF\):**

Given:
- \(ED = 5\)
- \(DF = 7\)

Using Pythagorean theorem in \(\triangle EDF\):
\[
5^2 + y^2 = 7^2
\]
Solve for \(y\).

**e) Triangle \(DEF\):**

Given:
- \(EH = 4\)
- \(HF = 9\)

Using properties of right triangles, assume \(EF = x\).

Using Pythagorean theorem in \(\triangle DEF\):
\[
x^2 = 4^2 + 9^2
\]
Solve for \(x\).

**g) Triangle \(ABC\):**

Given:
- \(AB = 6\)
- \(AC = 8\)

Using Pythagorean theorem in \(\triangle ABC\):
\[
x^2 + y^2 = 6^2
\]
With the information given vertical drop division, you may consider other properties or supplementary details such as similarity of smaller triangles.

Let me know if you need further assistance on calculating these!