To determine the most stable carbocation, we compare how effectively each structure can stabilize a positive charge.

For carbocations adjacent to nitrogen, stability depends strongly on whether the lone pair on nitrogen can participate in resonance donation into the empty $p$-orbital of the carbocation.

1. Key principle

A carbocation is highly stabilized if an adjacent atom with a lone pair can donate electron density:

This resonance delocalizes the positive charge and makes the carbocation much more stable.

So, the most stable structure will be the one where:

1. the positive charge is adjacent to nitrogen,
2. nitrogen has a lone pair available for overlap,
3. resonance delocalization is strongest.

2. Comparing the given options

The answer choices map as:

• A: $b$
• B: $d$
• C: $c$
• D: $a$

Among the four carbocations, structure $c$ is the one in which the carbocation is best stabilized by resonance with nitrogen lone-pair donation. Hence it is the most stable.

Its stabilization can be represented as:

This extra resonance stabilization makes it more stable than the others, which lack equally effective delocalization.

3. Final answer

Therefore, the most stable carbocation is $c$.

Since option C corresponds to $c$, the correct choice is:

4. Comparison with stored answer

Stored correct answer: C

Our derived answer: C

They match.