Step 1: Understanding the Question:
The question requires us to identify the correct preposition to fill in the blank and complete the sentence grammatically.
The blank is placed immediately after the adjective ``capable''.
Step 2: Key Concepts and Grammar Rules:
In English grammar, certain adjectives are followed by fixed prepositions.
This is known as prepositional collocation, where specific word pairings must be learned together.
The adjective ``capable'' is always paired with the preposition ``of'' followed by a gerund (verb ending in -ing).
Step 3: Detailed Explanation:
• Grammatical Rule: The structure ``capable + of + [noun/gerund]'' is standard English usage.
For example, we say ``capable of solving'', ``capable of doing'', or ``capable of great things''.
• Comparison with other options:
Option (A) ``in'', Option (B) ``with'', and Option (C) ``to'' do not collocate with the adjective ``capable''.
Using any of these three prepositions results in an ungrammatical and unnatural sentence structure.
Note that while we say ``able to solve'' (using an infinitive), we must use ``capable of solving'' (using a gerund).
Step 4: Final Answer:
Thus, the correct preposition to fill the blank is ``of'', making Option (D) the correct answer.