I don't have a sample but you can do what you ask using a controller and you will learn so much more building it yourself, like this:
First, all you need to do in your View is give each control you need to interact with an "id" - in this case your panel and your button. The controls in your view fire events that the Controller can capture and act upon
Now create a Controller if you don't already have one and then add a "References" for each control. E.g. if your button id is "myButton" then for the Reference name (step 1 of 1) enter "myButton" and for the selector (step 2 of 2) enter the button id with a "#' in front so "#myButton", make sure you spell these correctly. Do the same for the panel.
Okay, now in the Controller let's capture a "tap" event on the button - in the Controller add an "Actions - Controller Action". Choose "Ext.Button" for the target type and "tap" for the event name. Now you have a new function that will be called when you tap the button. Let's check that it works:
Select the new tap function in the Controller and switch to the Code view and enter "alert('Hello world');". Now save you project and run it - when you tap the button you should see a popup with the test "Hello world"
Ok, now we simply need to show and hide the panel when you click the button instead of displaying a popup message. To do that we need to be able to reference the panel so we can show and hide it - remember how we added a reference for the panel id earlier? Now we get to use that. Sencha helps us here in that it will automatically create a "getter" for us to access the panel. The name will be the word "get" followed by the id of your panel with the first letter captialized. So, let's say your panel id is "myPanel", you will use the function getMyPanel() to find the panel. Now we need a context to do it so use the word "this" which means the Controller:
So simply replace your alert message (or add to it) with the above line and now when you tap the button your panel should hide. You can show the panel using...
this.getMyPanel().hide(); // this will hide the panel
I think you'll be able to figure it out from there and sorry if I made any mistakes.
this.getMyPanel().show(); // this will show the panel