Step 1: Check grammatical structure. The given sentence in its original form (and options a, b, c) is either incomplete or awkwardly structured. They sound like sentence fragments.
Step 2: Review the options.
- (a) Incorrect: "Entertainment being recognized …" is incomplete; it lacks a finite verb.
- (b) Incorrect: Awkward and ungrammatical ("Recognition of it being … entertainment reduces …").
- (c) Incorrect: "Recognizing entertainment …" again is not a complete main clause; it leaves the idea hanging.
- (d) Correct: "Entertainment is recognized …" is a complete, clear sentence with subject + verb + object.
Step 3: Rewrite correctly.
The best standard form is:
"Entertainment is recognized as an important factor in improving mental and physical health and thereby reducing human misery and poverty."
\[
\boxed{\text{Entertainment is recognized …}}
\]