‘Like terms’ means things with the same letters.
Your question is: 14x - 14y + 7 - x + z + 2x
As 14x, -x and 2x all have the same letter; they are like terms.
The answer would be 3, as there are only 3 like terms in your question.
I hope this made sense, if you need any more help or need me to explain further just ask! :)