The key filter is "Received" in Message Direction. Here's a quick rundown on how to do it;
Go to Reports > Message Log Report
If you would like to see the list of all the messages received, filter by Message Log (recommended). This type of report will give you the list of all messages and not just a summary.
Enter a start and end date for the time period you want to see.
You can also choose to see only messages received linked to a particular campaign. If you want to do this, simply enter the name of your campaign.
Note: if you filter by campaign, your timeframe filter will be overridden!
Since you only want to see your inbound SMS, select Received.
From/ To Numbers
Unless you want to see inbound messages sent to a particular number, leave both with ALL selected.
Unless you want to see inbound messages containing specific keywords, leave this section blank.
Leave this section blank.
Once you are done, run the report.
Once the report has been generated, you can optionally email the report to yourself.
Reports that are under 10,000 records will be automatically generated. Larger reports will run in the background and will be emailed to you when ready.