We are given that the total length of line segment $FH = 10$, and the length of segment $GH = 8$. We are tasked with finding the length of segment $FG$.

To solve this, we use the relationship:

$FH = FG + GH$

We know that:

$FH = 10 \quad \text{and} \quad GH = 8$

Substitute these values into the equation:

$10 = FG + 8$

Now, subtract 8 from both sides:

$FG = 10 - 8 = 2$

Thus, the length of segment $FG$ is $2$.

Would you like more details or have any questions? Here are 5 related questions to further your understanding:

1. If $F, G$ and $H$ were collinear points on a number line, how would their coordinates relate?
2. How would the problem change if $GH = 5$ instead of 8?
3. Can you verify this result by drawing a diagram of the line segment?
4. What is the meaning of a line segment in geometry versus a line?
5. How can we express the relationship between the three points $F$, $G$, and $H$ using vector notation?

Tip: Always visualize the points on the line when solving geometry problems, as it helps clarify relationships between segments!