How are we best able to subject our ideas to the scrutiny of others?
Only by opening ourselves to information, insights, and critique from a variety
of different people

By eliciting insights and information relevant to understanding issues

By identifying, articulating, and applying reasoned responsive assessments of
issues, and take into account assumptions, facts, values, and perspectives of
others

Engaging in disagreement, questioning deliberatively, assessing the credibility
of information, and thinking critically

Your question can be efficiently answered with the following answer option: By identifying, articulating, and applying reasoned responsive assessments of issues, and take into account assumptions, facts, values, and perspectives of others

However, before answering this question, you need to know the meaning of the word "scrutiny." This word means "detailed thinking" and you can find that meaning in any dictionary or research platform. So we can understand that your question wants you to show how best to submit your ideas to people's detailed thinking.

The best way to present these ideas is presented in the answer option selected above. This is because this answer option shows that it is important that we identify our idea and that we work on it, before presenting it, that is, we must research our idea, structure it, evaluate issues that it can raise and how these issues can be resolved. All of this must be done with a strong foundation, which is achieved through well-produced research. This will allow people to understand our idea well and be able to evaluate it in depth, taking into account all the points we raised about this idea.

Not least, it is important that, after presenting our idea, we know how to consider and respect people's opinions about it. This avoids stress, unpleasant situations and can even enrich our ideas, because we can take those opinions and criticisms to improve the way we structure and present our idea to other people.

You can find more information in the following related question:

answer; decipher the motives for why people behave the way they do;