Step 1: Analyze the main clause. The main verb is 'promised', which is in the Simple Past tense. This is a reported promise.
Step 2: Apply the rules of reported speech. When the reporting verb is in the past, the verb in the subordinate clause also shifts. A promise about the future, often made with 'will' in direct speech (e.g., "I will work hard"), changes in reported speech.
Step 3: Determine the correct verb shift. In reported speech, 'will' changes to 'would'.
Step 4: Form the correct sentence. The correct completion is "would work". The sentence is: "Yogesh promised that he would work hard."