Two websites in the same niche

Hello guys, after the job interview received a test case to deal with. There are 2 websites owned by the company, and those two websites are in the same niche. To make it clear here's the example:

1. Website 1: http://www.beauty.com, and there is a subdomain http://www.blog.beauty.com
2. Website 2: http://www.beautynews.com

Guess what about writing http://www.beautynews.com and http://www.blog.beauty.com? Yep, about beauty news.
So what is the issue? I have to make an audit, provide fixes and make a strategy for http://www.beautynews.com. But I have no idea how to do this, how to growth this websites in regards of already existing http://www.blog.beauty.com. What to do to avoid cannibalization? Those websites belong to one company and should be growing both.
Please, help me with some ideas around this.

cannibalization refers to competing pages from the same site. If both sites target the same keyword they can both rank for that keyword, there's no canibalization in that

Regarding the site audit, there is software like Screaming Frog, Screpy, WebCeo and many others that can run site audits. You just let the software run, read the report and fix the errors / things that the report says, which can be many things such as: technical errors, broken links, on-page SEO, etc.

Regarding the strategy, I assume you mean a strategy for improving rankings. For that, you simply look inside of the GSC to see which URLs from the 2 websites are ranking on pages 2-3 on google, then you analyze your competition (preferably the first 5 URLs ranking in google for the same keywords that the URLs on your sites are ranking for on pages 2-3) and see if you can beat it, and how. Sometimes, optimizing the content (or adding a few 100s more words) will be enough, sometimes acquiring a few better backlinks than your competition is enough, sometimes it comes down to domain authority (in which case you need backlinks again, but really strong ones so you can up the domain's authority), other times it's all about fixing potential errors (that the aforementioned software finds when it runs audits), etc.... but you need to look at the competition first, and only then will you know how to tackle the issue.

Besides checking the GSC you could also find more long tail keywords that you can write content on. For established sites, writing content on long tail keywords almost always means instant ranking (or within days anyway) with good on-page SEO and a few internal links. Speaking of which, if your sites have URLs ranking on page 2 of google and you wish to push them to page 1 getting a few internal links (with exact match anchor) from more established pages could be enough.

There are more ways in which you can improve the rankings for established sites like yours seem to be, but in case you were referring to strategies for something else (not rankings improvement) then you need to specify what you're referring to

But anyway, running a site audit (and also checking the GSC as it can offer a lot of valuable insight) is probably where you should start

Aren't you posting on two different websites? So, there's really no keyword cannibalization to avoid.

I'd advise you to find a job you are qualified to do. Even if you nail the test and get the job, they'll understand pretty fast you are underqualified.