Hello Lily. You have made some great deductions, which lead you to the correct answer.
I would like to solidify the idea for you, so that the idea is more ground in understanding the science and the tool, LeChateller's principle.
Starting the chemical equation you have written out, if we convert the equation back into an uneven chemical equation (dropping charge and molar equivalents):
[Co(H2O)6] + HCl <==> [CoCl4]2- + H2O
we can now see a place for HCl (this is also where the Cl- originated from). Now if Cl- and HCl are approximately equivalent, and HCl is increased in solution, what will happen to the equilibrium, ideally?
As you concluded Lily, it will shift to the products (or to the right) side.