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Number the words as has been done in the previous comment
Initial configuration is {5,2,3,1,4,6}
Final configuration is {1,2,3,4,5,6}

Constructing a graph with edges between final position & initial position we have
1->5
2->2
3->3
4->1
5->4
6->6

1->5->4->1 , 2->2 , 3->3 , 6->6

The answer will be the total number of nodes - the number of disconnected components
Here the answer is 6-4=2

This can be explained as follows,
In a component(which is always a cycle) of 'n' nodes, n-1 swaps would be needed

Can the swaps occur anywhere, or for adjacent words only?

Just as you said, it is " similar to minimum swaps to convert string A to string B." so would we be given the string B in this case, which is "we must go to newyork now"?

1. If yes, then the decisive solution is same as conversion of string A to string B which takes some help from the Longest Common Sub-sequence dynamic prog problem.

2. If no, then I don't see if there is any decisive solution..

we can use inversion count approach
step 1: assign a number t each word of string A
and step 2: apply inversion count
geeksforgeeks archive : archives/3968

good solution bhavesh
@TechLead
We can assign a number to each word in the correct sentence
e.g.:
we must go to newyork now
we - 1
must - 2
go - 3
to - 4
newyork - 5
now - 6

do this using a map
now for the senetence spoken by yoda
"Newyork must go we to now"
create an int array storing numbers for the corresponding words
array would be {5,2,3,1,4,6}

count the number of inversions as done here: www[dot]geeksforgeeks[dot]org/archives/3968

The question of minimum number of swaps can be asked only if the resultant sentence(correct one) is given.

You see this in your mirror reflection