If in a certain language, $\text{CHARCOAL}$ is coded as $45164913$ and $\text{MORALE}$ is coded as $296137$, how is the word $\text{ALLOCHRE}$ coded in that language?

This is a direct substitution code where each letter is assigned a specific digit based on the given words:
From $\text{CHARCOAL}\to 45164913$:
$\text{C}=4$, $\text{H}=5$, $\text{A}=1$, $\text{R}=6$, $\text{C}=4$, $\text{O}=9$, $\text{A}=1$, $\text{L}=3$

From $\text{MORALE}\to 296137$:
$\text{M}=2$, $\text{O}=9$, $\text{R}=6$, $\text{A}=1$, $\text{L}=3$, $\text{E}=7$

Now substitute these values to decode $\text{ALLOCHRE}$:

* $\text{A}\to 1$
* $\text{L}\to 3$
* $\text{L}\to 3$
* $\text{O}\to 9$
* $\text{C}\to 4$
* $\text{H}\to 5$
* $\text{R}\to 6$
* $\text{E}\to 7$

Thus, $\text{ALLOCHRE}$ is coded as $13394567$.