You can use convert your “Month Name” slicer to the “Month Number” slicer. There’s an extensive “Date” created by @Melissa which provides you wide variety of options in date and if you’re using that Date table then you easily convert you slicer into “Month Number” .
I’m providing the screenshot below for the reference of my working.
You can use the traditional “Slicer” like @Harsh showed in his example where he just stretched the items out to where he didn’t have two rows. If you want multiple rows like you have shown, you will need to download the “Chiclet Slicer”. Here is how to do that:
Step 1
Step 2
Then you can edit the way the slicer looks to get your two rows. Here is what it looks like on one of my reports: