This question focuses on the correct usage of prepositions, which are essential words that show relationships between elements in a sentence, such as location, time, or manner. We need to select the most suitable prepositions to accurately complete the given sentence.

Prepositions in Context: Filling Sentence Blanks

The incomplete sentence is: "Rescue teams deployed _____ disaster-hit areas combat _____ a lot of difficulties to save the people." To fill the blanks correctly, we must consider the natural flow and meaning conveyed by different prepositions.

Deployment Preposition: Understanding the First Blank

The first blank follows the verb "deployed" and precedes "disaster-hit areas." This part of the sentence specifies the location where the rescue teams are sent or positioned.

• Deployed in: The preposition 'in' is typically used to indicate being inside or within a particular space, area, or region. For example, "soldiers deployed in the city." In the context of "disaster-hit areas," 'in' accurately describes the teams operating within these locations.
• Deployed to: While 'to' can indicate the destination or direction of movement (e.g., "deployed to the front lines"), 'in' is often preferred when describing the area where the deployment takes place and where operations are conducted.
• Deployed with: This preposition suggests accompaniment or using something as a resource (e.g., "deployed with advanced equipment"). It does not fit for indicating a location of deployment.

Therefore, "deployed in disaster-hit areas" is the most fitting choice, indicating the teams are situated and working within those regions.

Combat Preposition: Understanding the Second Blank

The second blank appears after "combat" and before "a lot of difficulties." This phrase describes how the rescue teams deal with challenges they face.

• Combat with: The phrase 'combat with' means to fight against, struggle against, or deal with something, especially an abstract challenge or opponent. For example, "combat with exhaustion" or "combat with unfair policies." It perfectly conveys the idea of facing and overcoming difficulties.
• Combat: The verb 'combat' can be used transitively without a preposition (e.g., "combat difficulties"), meaning to oppose or fight directly. However, when a preposition is used to emphasize the struggle against challenges, 'with' is a common and appropriate choice.
• Combat at: The preposition 'at' is generally used for specific points in space or time, or for specific states (e.g., "combat at close quarters"). It is not suitable for expressing the act of struggling against abstract difficulties.

Hence, "combat with a lot of difficulties" accurately conveys that the rescue teams are actively struggling against and overcoming numerous challenges.

Options Analysis: Selecting the Best Prepositions

Let's evaluate how each given option aligns with our analysis for both blanks.

Based on the analysis, the combination of 'in' for the first blank and 'with' for the second blank creates a grammatically correct and meaningful sentence. The complete sentence reads: "Rescue teams deployed in disaster-hit areas combat with a lot of difficulties to save the people."