Theory:

     Soapy believed that above his legs he looked all right. His face was clean. His coat was good enough. If he could get to a table, he believed that success would be his. The part of him that would be seen above the table would look all right. The waiter would bring him what he asked for.
 
     He began thinking of what he would like to eat. In his mind he could see the whole dinner. The cost would not be too high. He did not want the restaurant people to feel any real anger. But the dinner would leave him filled and happy for the journey to his winter home.
 
     But as Soapy put his foot inside the restaurant door, the head waiter saw his broken old shoes and the torn clothes that covered his legs. Strong and ready hands turned Soapy around and moved him quietly and quickly outside again.
Explanation:
 
Soapy thought of executing his first plan. The following scene takes place in front of a high-class restaurant. Soapy most likely thought he could cheat the restaurant staff by giving them the appearance of a gentleman.

Soapy thought he looked alright above his legs. 'He had a neatly shaven face, wore a good coat and a decent tie'.* Having confidence in his appearance, Soapy imagined a lavish meal ready for him. As it was a busy restaurant, Soapy thought that if he could get a table, the success would be his. He believed that he would appear great when he sat at a table. It meant that his upper clothing gave him the appearance of a gentleman, but his lower clothing gave him the impression of a poor man because he was wearing broken shoes and torn pants. Later, he imagined that he would order a delicious dinner if he could get a seat, and the waiter would bring him what he asked for.
 
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Soapy had a neatly shaven face, wore a good coat and a decent tie*
 
Soapy was assuming everything in his mind by standing outside the hotel, like what food to eat. He could see the whole dinner in his mind. 'He thought of ordering food like a roasted mallard duck, Camembert, and a demi-tasse'.** Here, Soapy decided to eat well, but not so expensive as to raise suspicion or make hotel management to take severe actions, but just enough to get him arrested by a cop as planned.
 
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Soapy thought of ordering food like a roasted mallard duck, Camembert, and a demi-tasse** (left to right)

Soapy's desire was not only to enjoy a wonderful meal but also the way for going to prison. If his wish became true and his plan gets succeeded, it would easily pave the way for his journey to his winter home (prison).

Having decided to enter the restaurant, Soapy put his foot inside the restaurant door. At that time, the head waiter standing near the door saw Soapy's broken shoes and torn clothes covering his legs. Immediately, he was sent out of the restaurant by the "strong and ready hands". The phrase "strong and ready hands" meant that the head waiter moved Soapy immediately out of the restaurant without letting him in. The head waiter silently turned Soapy and quickly moved him outside. The tattered shoes and damaged clothing reflected Soapy's reality in front of the head waiter. At last, his first plan had flopped (failed).
 
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The strong and steady hands pushed Soapy out
 
Meanings of the difficult words:
 
S.No
Words
Meanings
1
Success A person or thing that achieves desired aims
2
Waiter A man whose job is to serve customers at their tables in a restaurant
3
AngerA strong feeling of annoyance, or displeasure
4
Journey An act of travelling from one place to another
5
FloppedA plan become completely unsuccessful or fail totally
Reference:
National Council of Educational Research and Training (2007). Supplementary. The Cop and the Anthem- O. Henry(20-29). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.