Being able to edit the Google Analytics account is the 2nd highest permission level. You need this if you want to create a new web property in Google Analytics.
To grant permissions to another user you will need the highest permission level yourself: being able to manage users on the account.
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Step 1: Go to account user settings page
First click the admin cog in any view under the account in GA you want to change, and then in the left hand list go to User Settings
Add a new user's email (must be a Google account) and check the 'edit' checkbox.
Step 3: Check it's working
Your colleague should now be able to see 'Create new property' under the list of properties in the middle of the Admin page.