In the given sentence, the main verb is: 'is'. The word, 'happy' is an adjective. The phrase 'to+verb' (also called infinitive) after an adjective is used to present the reason for something. The phrase, 'to see his son's excellent result' gives the reason for the phrase, "Mr. Ghosh is happy'. The correct sentence is: 'Mr. Ghosh is very happy to see his son's excellent result'. Option B is correct.
Option A: The preposition phrase, 'for+verb-ing' can modify a noun or a verb. For example: 'Mr. Ghosh's son got praised for working very hard'. Here, the phrase 'for working very hard' modifies the verb 'praised'. The phrase, 'for seeing' cannot be used to modify an adjective ('happy' in the given sentence). Hence, option B is incorrect.
Option C: The phrase 'by+verb-ing' is used to indicate how a certain thing happened/ was achieved. For example: Mr. Ghosh's son got excellent results by working hard'. Here, the phrase 'by working very hard' modifies the verb 'got excellent results'. In the given sentence, the phrase, 'by seeing' cannot be used to modify an adjective ('happy' in the given sentence). Hence, option C is incorrect.
Option D: The sentence, 'Mr. Ghosh is very happy sees his son's excellent result' is grammatically incorrect. The verb 'sees' cannot be used immediately after the clause, 'Mr. Ghosh is very happy'. It needs to be connected with a conjunction/ preposition/adverb. For example: 'Mr. Ghosh is very happy after he sees his son's excellent result' is a correct sentence. Hence, option D is incorrect.