Is using »um« in this sentence correct?

Question

I request you to understand this Problem. Can we write it in both ways while writing a formal letter?

Ich möchte Sie um Verständnis dieses Problem bitten.
Ich bitte Sie, dieses Problem zu verstehen.

Answer 1

This is correct:

Ich möchte Sie um Verständnis für dieses Problem bitten.
^{I would like to ask for your understanding for this problem.}

• Ich möchte Sie ... bitten = I would like to ask (you)¹
• um Verständnis = for (your)¹ understanding
• für dieses Problem = for this problem

¹_{In German you indicate the person who is asked in an accusative object (ich möchte Sie bitten), while in English you provide this information in an attribute of understanding (for your understanding)}

Um etwas bitten: Here etwas is the thing you want to get.
Für etwas/jemanden bitten: Here etwas or jemand is the thing or person to which you want to apply what you hope to get:

Ich bitte um Wasser für meine Blumen. = Ich bitte für meine Blumen um Wasser.
I ask for water for my flowers.

The different prepositions gives you the change to swap the two parts without creating any confusion. You can't do this so easily in English.

---

But the two sentences in your question have different meanings:

1. Ich möchte Sie um Verständnis für dieses Problem bitten.

   Here you ask for empathy. You presume that the nature of your problem is obvious to the other person, and now you ask for sympathy for your way to deal with it.

2. Ich bitte Sie, dieses Problem zu verstehen.

   This can be understood similarly, but it also has this meaning:
   The nature of your problem is complicated and needs lots of explanation. And the addressee of your message also must be willing to concentrate and think through the many complicated steps to be able to decode and recognize your problem. So, here you ask the other person to spend time and brain power to follow your explanations.