The function of the
that-clause is direct object of
believe.
Believe
what? Believe
that you like it.
The
that-clause can also be considered the direct object of the
find construction.
Note the grammar of
find.
I find this difficult. (
this is the direct object of
find. Find
what? Find
this.)
With the object preposed:
This I find difficult.
Now suppose the adjective complement is extended with an infinitive thus:
I find this [difficult to believe]. (Find what? This. Believe what? This.)
Object preposed:
This I find [difficult to believe].
In your example sentence
this is replaced by
that you like it:
I find that you like it [difficult to believe].1 (I find the fact that you like it ...)
Object preposed:
That you like it I find [difficult to believe].
CJ
1This turn of phrase is almost never used. Instead, anticipatory
it replaces the object of find, which is postposed.
I find it [difficult to believe] that you like it.