It seems that your post has been victim to the fact that this forum uses markdown. The double asterisks are used to indicate bold. Thus, I will need take a guess on what you had originally. Also, I don't have access to SQL Server Compact, so this is only tested on regular SQL Server:
DECLARE @text varchar(50) = 'Potatoes ** will expire in 2022 in inventory'
DECLARE @specific varchar(20) = '**'
SELECT left(@text, charindex(@specific, @text) - 1)
You can use the button with ones and zeroes to insert code (which will evade the issue with the double asterisks being gobbled up), or select piece of text to press CTRL/K to the same effect. Use the Preview button to check the result before you submit.