Are you not allowed ask suggestions for other websites because its considered 'soliciting'?

It depends on the wording of the question or answer being given. If you are asking for sites to watch copyrighted material illegally, for example, that is a violation. Not for solicitation, but for asking for illegal links. Other types of requests can be seen as solicitation, for example, "Is this a good site to use?" with a link on it or "Is this a funny video?" with a youtube link.

If I am deciphering your English correctly, you want to know if in your question you can ask for others to suggest websites, and if this is a form of solicitation. This is a somewhat complicated matter because like many questions that are not cut and dry it falls within the more grey areas of community guidelines.

My first reply to you is this: Your question may not be a violation, but the answers will be. Thus, unless you are lucky, and nobody catches it, you may get an answer that is useful for you.

However, if someone begins reporting the answers they may feel justified in reporting your question as a violation by assuming you were coaxing solicitation of websites, which can be construed as a form of exploitation. You would then need to appeal the violation, which can leave you mired in muck.