hard time of +ing or hard time +ing ?

She had a hard time explaining the situation.
She had a hard time of explaining the situation.

Hello! What of sentences written above is more correct for you and why? In addition to those sentences given above I think it would be better if I give you some more to clear my problem.

  1. I created The 9 back in 2008. The original venue was DC9, which is where the number of 9 came from. The 9 was created because Adrian(Krygowski) and myself and all of our peers around town, even in our prime drawing areas we may have a hard time of getting into clubs that we really want to get into.
    (! have a hard time of getting !)
  2. I have a hard time going to school because I’m so behind? or I have a hard time accepting that those who do not believe will perish.
    (! a hard time going !) and (! a hard time accepting !)
  3. We have difference ways of solving this problem.
    (! ways of solving !)
  4. Have you any reason for saying such a thing ?
    (! reason for saying !)
    all these gerunds are used like an attribute for the words they(gerunds) follows but why some of people use a preposition between “a hard time” and a gerund and other don’t do it ?

p.s. and feel free to correct my mistakes in my sentences if any!

The first is correct. The second is incorrect.

  1. ‘have a hard time of getting’ is incorrect. The ‘of’ should not be used.
  2. These are correct.
    The first one means I find it difficult going to school/I find it difficult to go to school.
    The second one means I find it difficult accepting / I find it difficult to accept.
    3)have difference’ is incorrect. The sentence should read ‘We have different wats of solving this problem’ or ‘we have different ways to solve this problem.’
  3. This is correct. It means the same as ‘have you any reason to say such a thing’.

There is a very long thread about this here:

does it mean a native speaker who said the sentence ‘have a hard time of getting’ is ignorant of how to use a gerund?

The person who said those words in interview may be considered a fine songwriter and talented musician, but he was speaking extremely colloquially, at least on that occasion. I presume that his words were written down verbatim in the interview. He spoke with what I would consider to be a ‘hip-hop street culture style’ which does not follow the rules of standard grammar.

The ‘of’ is used incorrectly, not the gerund.
He also said ‘the number of 9’ which is incorrect. No ‘of’ is required there either.
His final sentence quoted above is not even a sentence. The beginning is not resolved.