We use the phrase "get around to sth/ to doing something" to express that we finally do someting that we have intended to do for some time.

Example:
I meant to call you yesterday, but I didn't get around to it.

In the picture below, you will find some more examples that will help you to better understand how to use this phrase.

To download and save this picture : right-click on the image and choose Save Image As or Save Picture As. 

We use the phrase " to get down to sth / to doing sth" to express that we start to direct our efforts and attention towards something.

Example:

I always find it hard to get down to studying at night.

In the picture below, you will find some more examples that will help you to better understand how to use this phrase.

To download and save this picture : right-click on the image and choose Save Image As or Save Picture As.