X's and O's

Steps 1. and 3. increase the length of a string by one character and step 2. decreases the length of a string by one character. So to go from a string of length $3$ to one of length $6$ we must use steps 1. and 3. a total of $n \ge 3$ times and step 2. a total of $n - 3$ times for a total of $2n - 3$ steps, which, being odd, rules out $4$ and $6$ as possible choices.

Now although $3$ is not an answer option, we should first, in the interest of completeness, rule it out as the actual minimum. To increase the length of a string by $3$ characters in $3$ steps would mean that we can only use steps 1. and 3.. Given this restriction, the only way to increase the number of $O$ 's by two and the number of $X$ 's by one would be to employ step 1. twice and step 3. once. But none of the three possible such sequences of steps would result in a string beginning with " $OX$ ", and so the desired transformation cannot be achieved in $3$ steps.

To achieve the transformation in $5$ steps, one possible sequence is to apply step 3. three times to get $XXXOOX,$ then apply step 1. to get $XXXOOOX.$ From here we apply step 2. to end up with $OXOOOX,$ the desired string.

1- replace (oo) with (xoo) three times (three steps ) you will have (xxxoox) 2- replace (xxx) with ox (one step) you will have (oxoox) 3- replace the first (x) with (xo) (one step ) final result is (oxooox ) sum of steps is five

INITIAL: OOX, STEP 1: XOOX, STEP 2: XXOOX, STEP 3: XXXOOX, STEP 4: OXOOX, STEP 5: OXOOOX,