Hello Brassdragon
The choice between the prepositions
à and
de is often difficult for English speakers learning French. This is because more or less, you must simply memorize which preposition is part of which expression/structure.
There are two separate structures here with "difficile," and they are not grammatically equivalent. As it happens, one requires
de and the other requires
à. I'm basing this answer on the TLF dictionary entry for
difficile.
1. impersonal expression
...a. il est (c'est) difficile
de + infinitive phrase saying what is difficult
...b. c'est difficile
à + infinitive with no phrase, absolute usage.
2. difficile
à + infinitive of a transitive verb
When you say
Je trouve cela difficile à comprendre, you are in case two. You're using
difficile à comprendre as an
adjective phrase to describe
cela. You must use the preposition "à." You're saying, "I find that hard to understand" where "hard to understand" describes "that." You could also say "That's hard to understand" =
C'est difficile à comprendre. You would still be using "hard to understand" to describe "that." It is this adjective-like structure that dictates "à" for expressions with
difficile.
When you say
Je trouve difficile de comprendre cela, you're really saying a shortened version of
Je trouve qu'il est difficile de comprendre cela. This puts you in case one, so you must use the preposition "de." You don't have an adjective phrase describing "that" this time. Instead, you are implying the structure "it is difficult to do X". For this
impersonal structure with
difficile, you need to use "de."
You can read more examples in the dictionary link I gave above.
As I said, there is no rule to predict which verbs require
de and which ones require
à in which situations. Expressions with
possible will not necessarily use the same prepositions as expressions with
difficile.... though it does happen that the correct expression for impersonal constructions with
possible is
il est possible de + infinitive phrase saying what is possible. Since each thread should talk about only one expression, please let's not discuss
possible here (though you are welcome to open a separate thread, or see
here).
Since the topic in general can be confusing, we've had lots of discussions about it. If you're interested in which preposition to use with a given expression/phrase, try looking it up in the dictionary or on the forums. For example, I have transferred your question into an existing thread about "difficile"... so you might want to read back through the previous posts.
There is also an article in French cited
here in our Resources forum...
I hope it helps!