This works for me on the Northwind sample DB, note that SearchLetter has 2 characters to it and SearchLetter also has to be declared for this to run:
declare @SearchLetter2 char(2)
declare @SearchLetter char(1)
Set @SearchLetter = 'A'
Set @SearchLetter2 = @SearchLetter+'%'
select * from Customers where ContactName like @SearchLetter2 and Region='WY'