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If I'm understanding you right, you aren't able to see the presenter display on your iPad when play the presentation on your external monitor. I know how important it can be to be able to see presenter notes, slide numbers, etc. I'm happy to provide you with some guidance on doing so.
From the picture you attached to your post, it looks like you're connecting your iPad to your external monitor via a Lightening to VGA adapter. As long as everything is connected and set up correctly, the presenter display should automatically appear in the presentation displayed on your iPad. Make sure these are the steps you are taking:
- Connect an external display to your device using AirPlay or a video adapter. If you’re using Apple TV, turn on mirroring.
2. Tap ► in the toolbar.
Your presentation begins to play on the connected display, and Keynote on your device switches to show the presenter display.
A green light next to the slide number on the presenter display indicates that the last transition or build effect on the current slide has finished playing, and you can tap the slide to advance to the next build or slide.
A red light next to the slide number indicates that a slide transition or slide build hasn’t finished playing; you can’t advance to the next build effect or the next slide until the current transition build is completed.
3. To exit the presenter display and stop playing your presentation, pinch the slide or tap ✕."
Keynote for iPad: Play a presentation on a separate display
If these are the steps you're taking and it still isn't working as expected, I recommend making sure your iPad devices software is up to date: Update your iPhone, iPad, or iPod touch. Next, install any available updates for Keynote. To do so, go to the App Store on your iPad, then tap Updates. If an update is available, tap Update. If everything is already up to date or it still isn't working after updating, take a look at the steps under the "If you need help with other issues" section at the bottom of this support article: About Apple Digital AV Adapters for iPhone, iPad, and iPod touch.
Once you get things working like expected, you may find the following resource helpful when using Keynote on your iPad: Keynote Help for iPad.
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Take care!