Learn English – Difference between free and gratis

The only verb that means "working in a certain way" is operate; the other verbs have different meanings.

For example, implement means "to make something that has been officially decided start to happen or be used."

A new work programme for young people will be implemented.

The regulations implement a 1954 treaty.

When speaking of code, I could say "I will implement the new program features over the next week."

As phrasal verb, carry out means "to do something that you have said you will do or have been asked to do" or "to do and complete a task."

Your examples are mixing two senses of the word challenging. The entry in Slovar-vocab is wrong when it states "stimulate" is a synonym of "challenge" when it means "something difficult".

1. The book I read stimulated me.
2. The book I read challenged me.

In sentence 1, the book is thought provoking or inspired interest in a topic.
In sentence 2, the language of the book was difficult and it took a lot of effort to read, or it forced me to confront my thinking about something and it was a little uncomfortable for me to realize that maybe I need to change my opinion or understanding. It's not clear from the context which meaning is the intended one.

One interesting thing to note is that while "stimulating" is sometimes listed as a synonym for "challenging", the opposite isn't usually true. They are only related through the word "provocative" which has two meanings:

1. Serving or tending to elicit a strong, often negative sentiment in another person; exasperating.
2. Serving or tending to excite, stimulate or arouse sexual interest.

"Stimulating" is provocative in a positive sense, but without necessarily the sexual connotation, like "exciting". "Challenging" can mean provocative in a negative sense, like "defiant" or "disturbing", but it usually means "difficult to do".