Step 1: Understanding the archaeological sites and their corresponding periods.  
- Soan Valley (A): The Soan Valley is known for its Lower Paleolithic sites, where early humans used simple tools. These date to about 1 million years ago. Therefore, it matches with (III) Lower Paleolithic.  
- Bhimbetka (B): Bhimbetka is a well-known site for Mesolithic cave paintings, which show the development of early human art and tools after the Paleolithic era. Hence, it corresponds with (II) Mesolithic.  
- Sarai Nahar Rai (C): This site is associated with the Upper Paleolithic period, which marks the end of the Stone Age, where more sophisticated tools were created. Thus, it aligns with (I) Upper Paleolithic.  
- Daojali Hading (D): Daojali Hading is associated with the Neolithic period, which saw the advent of agriculture, pottery, and permanent settlements. Hence, it fits with (IV) Neolithic.  
Step 2: Conclusion.  
The correct matching is:  
- Soan Valley: Lower Paleolithic  
- Bhimbetka: Mesolithic  
- Sarai Nahar Rai: Upper Paleolithic  
- Daojali Hading: Neolithic  
  
 Final Answer:  
\[
\boxed{\text{The correct answer is (2) (A) - (III), (B) - (II), (C) - (I), (D) - (IV).}}
\]