On Snapchat you can find out how many snaps you have sent or received by looking on your profile page.
Steps

Step 1. Open Snapchat
This is the icon of a white ghost on a yellow background. The application will open on the camera page.

Step 2. Slide the screen down
You will reach your profile page.
You can also click on the ghost in the upper left corner of the screen

Step 3. Click on your username
It's in the middle of the screen, below your display name. It will be replaced by two numbers separated by a vertical line.

Step 4. Read the numbers of snaps sent and received
The number on the left corresponds to the number of snaps sent and the number on the right corresponds to the number of snaps received.