Select the most appropriate option that can substitute the underlined segment in the given sentence.

We must remember that what we teach our children is what we inculcate in them.

To find the most appropriate option to substitute the underlined word "inculcate", let us analyze the meaning of the word in the context of the sentence:

Sentence: "We must remember that what we teach our children is what we inculcate in them."

The word inculcate means to instill or teach an attitude, idea, or habit by persistent instruction or repetition. In this context, it refers to firmly establishing a habit or belief in a child's mind.

Now let's examine the options:

1. endanger: to put someone or something at risk or in danger. This is irrelevant to teaching or teaching values.
2. inspire: to fill someone with the urge or ability to do or feel something. While related to teaching, it does not specifically mean to introduce or implant a quality gradually.
3. instil (or instill): to gradually but firmly establish an idea or attitude in a person's mind. This is a direct synonym of "inculcate" and fits perfectly in the context of teaching children.
4. import: to bring goods or services into a country from abroad, or to convey a meaning. This does not fit the context.

Therefore, the word that best substitutes "inculcate" is instil.

The correct option is instil.