Given a String S1 and String S2. Convert string S1 to a palindrome string such S2 is a substring of that palindromic string. Only operation allowed on S1 is replacement of any character with any other character. Find minimum number of operations required.
Here is a description of a simple brute force approach that works in $O(n^2)$, where $n$ is the length of $S_1$.
Let $m$ be the length of $S_2$. If $m>n$, return -1 immediately, indicating impossibility.
Keep a counter on how many characters will be changed. Change $S_1$ so that its substring with length m that starts at index 0 is the same as $S_2$. Mark the indexes where characters have been changed. Also chang $S_1$ so that ist substring that starts at index n-1-0 and goes backwards to index n-m-0 is $S_2$ backward. However, abort this try if we have to change the characters that has been marked. Now change the remaining characters of $S_1$ to make it a palindrome. That is, if the character at index $i$ is not same as the character at index $n-1-i$, change the later to be the former. Once done, the counter tells us how many changes is needed to make $S_1$ a palindrome that has $S_2$ as its substring starting at index 0.
Repeat the above with index 0 replaced with index $1, 2, \cdots, n-m$, keeping tracking of the minimal number of changes.
The above description should be enough to set you up. You may want to improve it or look for better algorithms.