If Thompson appeals to moderates, his most ardent supporters will desert him and he will not have enough votes to win the election.
Evidence
If Thompson appeals to moderates, his most ardent supporters will desert him and he will not have enough votes to win the election. TAM → ~WE
However, if he does not appeal to moderates, these moderates will vote for his opponent and he will not have enough votes to win the election. ~TAM → ~WE
Conclusion
Either way, Thompson is bound to lose the election. ~WE
Evaluate
There aren't any clear premise or conclusion indicators in this argument. However, two of the statements in the argument are conditional statements. The final sentence is a prediction about the future which is based on those conditional statements. Predictions in LSAT arguments tend to be conclusions, and the overall structure of this argument points to the final sentence being the conclusion.
The conditional statements in the evidence describe a binary choice: Thompson can either appeal to moderates or not appeal to moderates. The evidence states that either choice will result in Thompson not having enough votes to win the election.
The conclusion confirms the outcome indicated by the evidence: it states that Thompson will lose the election.
Goal
Look for an answer which describes a binary situation where either option will result in the same outcome. The conclusion will confirm that outcome. Beware of answers with evidence describing a situation that is not actually binary—a situation where there are more than two possibilities. Also beware of answers with conclusions that don't simply confirm a necessary outcome that's described in the evidence.