A simple program using branching to guess the answer
I think in general this is fine. The only things I'd point out are stylistic really.


In Ruby, many people would prefer double-quoted strings, which allow you to: Got it; your number is #{number}, right?. Note that this also relies on an implicit #to_s on number. It also allows single quotes to be used without escaping. 
Look out for variable naming. Naming things correctly is notoriously hard, even after years of experience, and number is a bit generic.
I would definitely put the if conditional on the same line as the if. If the expression is too long or a bit difficult to instinctively understand, assign its value to a variable with a meaningful name (e.g. correctly_added_six = number_plus_6.to_i == number.to_i * 2 + 6) so your condition is more easily understood (e.g. if correctly_added_six)


Good start, though!