To make your Steam inventory public follow the steps below.
Step 1.

Login to the Steamcommunity website.

Go to Steam and click the login button on the top right corner of the page.

Enter your username and password and click "sign in" button.

Step 2.
Enter your profile page.

To enter your profile page, click the button with your nickname and click view profile.

Step 3.
Click the edit profile button.

Step 4.
Go to privacy settings.

Step 5.
Change status and inventory settings to "public" and save changes.