I have seen the phrase that of being very commonly used, but I have never seen the phrase that from. Does the following sentence makes sense?
The number of words recalled from the list of food was compared to that from the list of cities.
The longer version of that sentence is:
The number of words recalled from the list of food was compared to the number of words recalled from the list of cities.
Essentially, the word that replaces the phrase the number of words recalled. Is this acceptable?
It is acceptable and correct to say so.
This might be of interest to you: What's the exact usage of "that of"
and this: https://ell.stackexchange.com/questions/15425/what-does-that-of-mean
An example: "I've compared this piece of text with that of John's."
A bonus explanation of compared to/compared with:
http://grammarist.com/usage/compared-to-or-compared-with/
Compared with is usually referring to two objects of similar classification (e.g., dogs to dogs and cats to cats). Within this similar order, the user is speaking of the differences between the two objects of comparison.
Compared to is referring to two items in different classifications (e.g., dogs to cats or cats to cars). In these differing classifications, the user is pointing out similarities between the two seemingly unrelated objects.
