Use conjective symbols and the nine valid inference rules MP, MT, SIMP, CONJ, ABS, ADD, DS, HS
Either animals are mere mechanisms (M) or they feel pain (P). If either animals feel pain or they have souls (S), then they have a right not to be subjected to needless pain (R) and humans have a duty not to inflict needless pain on them (D). It is not the case that animals are mere mechanisms. Thereofore, animals have a right not to be subjected to needless pain.
Okay, the first thing you've got to do is break down your argument into its component statements. Next, identify the conclusion (keywords, "so," "therefore," "as a result," etc.), and the leftover statements become your premises. Next, determine the simple (atomic) statements in each compound statement. You can do this easily given the fact that you've got your symbolic letters. Finally, circle your connectives so you can see how the compound statements are built, and further what symbols go with what connectives. In different logic systems you'll get ...
The solution provides a conversational reponse teaching how to formulate and format these kinds of argument, then applies it to the question in hand. 360 words.