Correct spelling, explanation: the word conductor is created by adding a suffix to a base word conduct. The main difficulty you face when choosing a suffix in conductor is that the suffix -or can take the form of -er or -ar and it may not be clear which one should be used where. For example, there is a seller from sell, or a liar from lie. In the case of words ending in ct, you should add an or suffix, like in investor which comes from invest.

Definition of conductor:
noun
1. someone responsible for collecting tickets or fares on public transport
I didn’t have a ticket nor money but fortunately, it was so rainy and cold that the conductor let me stay on the train.
2. a person in charge of guiding the orchestra
The conductor had a black tuxedo and a white shirt; the orchestra started playing as soon as he moved his hands.
3. In chemistry and physics, a substance that allows for carrying electric current
Metals are usually good conductors which is why they are used to create wires.

Incorrect spelling, explanation: there is some confusion about when to use the suffix -er and -or when creating a noun representing a person who does an action. There are specific rules to tell you why conducter is an incorrect word, but more practically – think of the word of a similar structure. The base word here is conduct, and think of the two last letters: ct. Find a similar word: act. Think of a similar noun: actor. And by the same logic, you can derive conductor and know that conducter is not right.