(a) difficulty/trouble/problem

1a. I have a difficulty understanding what he is saying.
1b. I have difficulty understanding what he is saying.
2a. I have a trouble understanding what he is saying.
2b. I have trouble understanding what he is saying.
3a. I have a problem understanding what he is saying.
3b. I have problem understanding what he is saying.
Please correct all.
Thanks.

To me, the article does not seem to be necessary unless you have some particular personal difficulty/trouble/problem in understanding what he says.

I would agree with Anglophile regarding #1.
No article for #2 in any situation.
The article is necessary with ‘problem’ in #3 unless you change it to ‘problems’.

Beeesneees, Anglophile,

  1. I have (a) difficulty(CN) (in) understanding what he is saying.
  2. I have (X: a) trouble(UN) (in) understanding what he is saying.
    3a. I have a problem (in) understanding what he is saying.
    3b. I have problems (in) understanding what he is saying.
    In all these sentences do you consider ‘in’ is optional or compulsory?
    Note:
    CN = countable noun
    UN = uncountable noun.
    Please comment.
    Thanks.

The nouns ‘difficulty’ and ‘trouble’ are found used as both count and noncount nouns. The NSE could differentiate them better. ‘In’ is optional.

You have already received answers from great teachers. What I can add is as follows:

   Although the nouns [i]difficulty[/i] and [i]trouble[/i] can be both countable and uncountable, in the expressions [i]have difficulty/have trouble[/i] both the nouns are used as non-count. (We [b]usually[/b] say 'have difficulty' and [b]never[/b] say 'have a trouble', thus, as Beeesneees said

‘In’ here is correct but optional in all cases. It is normally omitted in daily conversational use.

   Thanks.

Foreigner,

  1. I have trouble fixing the car.
  2. I have trouble in fixing the car.
    Do you consider both are correct?
    thanks.

Yes! They are absolutely correct!

You have already received answers from great teachers. What I can add is as follows:

   Although the nouns [i]difficulty[/i] and [i]trouble[/i] can be both countable and uncountable, in the expressions [i]have difficulty/have trouble[/i] both the nouns are used as non-count. (We [b]usually[/b] say 'have difficulty' and [b]never[/b] say 'have a trouble', thus, as Beeesneees said

‘In’ here is correct but optional in all cases. It is normally omitted in daily conversational use.

   Thanks.