Let's break this down step by step.

The problem says:

• $G$ is between $E$ and $H$, and $F$ is the midpoint of $EG$.
• Given $FH = 11$ and $FG = 3$, we are to find the total length of $EH$.

Step-by-step solution:

1. Relationship between points:

   • $F$ is the midpoint of $EG$, so $EF = FG$.
   • From the problem, we know $FG = 3$, so $EF = 3$.

2. Total length of $EG$:

   • Since $F$ is the midpoint of $EG$, the total length of $EG$ is $EF + FG = 3 + 3 = 6$.

3. Use given information about $FH$:

   • We know that $FH = 11$.
   • The total length of $EH$ is the sum of $EG$ and $GH$. We already know $EG = 6$, so: $EH = EG + GH = 6 + 11 = 17$

Thus, the length of $EH$ is 17.

Would you like any further explanation or details? Here are some follow-up questions you might find helpful:

1. How do you determine the midpoint of a line segment mathematically?
2. Can you generalize the formula for finding the length of a line segment when given partial distances?
3. What is the significance of using the midpoint in geometric problems?
4. How can you check your work when working with segment addition in geometry?
5. How do you handle more complex geometric figures with multiple midpoints?

Tip: Remember, in problems involving midpoints, the segment is always divided into two equal parts!