My JLPT practise book has these two sentences to help explain the difference between お目{め}にかける and お目{め}にかかる in a context of keigo.

それでは新製品{しんさくひん}お目{め}にかけましょう。

鈴木{すずき}さんという人{ひと}に初{はじ}めてお目{め}にかかりました。

Unfortunately, the brief explanation they give about these sentences is not quite enough for me to be sure I've got it.

I think the first case, お目{め}にかける is when you're asking someone else to look at something. "Please look at X."

And I think the second case of お目{め}にかかるis when you're doing the looking. "I saw X."

I often get these kinds of differences mixed up. Can someone either confirm I'm right, tell me if and where I'm wrong, or enlighten me if there is some other nuance I should be aware of?

My JLPT practise book has these two sentences to help explain the difference between お目{め}にかける and お目{め}にかかる in a context of keigo.

それでは新製品{しんせいひん}お目{め}にかけましょう。

鈴木{すずき}さんという人{ひと}に初{はじ}めてお目{め}にかかりました。

Unfortunately, the brief explanation they give about these sentences is not quite enough for me to be sure I've got it.

I think the first case, お目{め}にかける is when you're asking someone else to look at something. "Please look at X."

And I think the second case of お目{め}にかかるis when you're doing the looking. "I saw X."

I often get these kinds of differences mixed up. Can someone either confirm I'm right, tell me if and where I'm wrong, or enlighten me if there is some other nuance I should be aware of?