Step 1: Understanding the rule
The rule says:
An alveolar nasal [n] becomes dental [n] when it appears before a dental fricative [\(\theta\)] or [\(\sigma\)].
- \([+alveolar, +nasal]\) = [n] (alveolar nasal).
- \([+dental, +fricative]\) = [\(\theta\)] (voiceless dental fricative) or [\(\sigma\)] (voiced dental fricative).
So, whenever [n] occurs before [\(\theta\)] or [\(\sigma\)], it becomes dental.
Step 2: Checking the options
- (A) \emph{panther} → contains [n] followed by [\(\theta\)]. This looks like a candidate, but note: the [n] here is alveolar nasal before [\(\theta\)]. This word can indeed undergo the change.
- (B) \emph{length} → contains [n] before [\(\theta\)]. This is the clearest and most common example of this rule in English. The alveolar nasal [n] assimilates to dental [n] before [\(\theta\)].
- (C) \emph{warmth} → has [m] before [\(\theta\)]. But [m] is bilabial nasal, not alveolar nasal. Rule does not apply.
- (D) \emph{another} → has [n] before [\(\sigma\)]. Since [\(\sigma\)] is a dental fricative, the alveolar [n] becomes dental [n]. This is also a possible application.
Step 3: Choosing the best answer
While both (B) \emph{length} and (D) \emph{another} technically satisfy the condition, in phonological rule illustrations, the most standard textbook example of alveolar nasal assimilation before a dental fricative is \emph{length}.
Step 4: Conclusion
Therefore, the correct answer is:
\[
\boxed{\text{Correct Answer: (B) length}}
\]