Given the line segment $EH$, $EH = 26 - x$, and other information about the segments:

1. $FH = 12$
2. $EG = x + 23$

To find $EG$, we need a little more clarification about the geometric relationship between these line segments. For example, are $EH$, $FH$, and $EG$ part of the same line, or are they connected in some other way, like forming a triangle?

If we assume that $EH$ is part of a line that contains both $EG$ and $FH$, we might need more information to solve for $x$. Could you provide more context or clarify the arrangement of these segments?

Let me know if you'd like to provide further details, and I'd be happy to help. Here are 5 possible questions to extend this situation:

1. What is the total length of the line that contains $EH$, $FH$, and $EG$?
2. Are these segments part of a triangle or some other shape?
3. Can we solve for $x$ from another equation involving $EH$ and $EG$?
4. Are there any additional segments or relationships between points $E$, $F$, $G$, and $H$?
5. Is there any other information given about angles or distances between these points?

Tip: Always look for the relationships between segments, whether they're collinear or form other geometric shapes, to set up proper equations.