Firstly, what you have written there is a proposition, not an argument. An argument has premises and a conclusion. What you are asking is how do we interpret the quantifier scope in propositions that have more than one quantifier. The short answer is to read the proposition left-to-right and take the leftmost quantifier as having wider scope. So,
(∀y)(∃x)Ryx should be read as: for any y...there is some x such that...Ryx.
On the other hand,
(∃x)(∀y)Ryx should be read as: there is some x such that...for any y...Ryx.
The two mean different things: if we restrict the quantifier y to range over rats, and x over tails, then the first can be interpreted to mean every rat has a tail, while the second would mean there is some one tail that every rat has.
If that is not sufficiently clear, think of each successive quantifier as being parenthesised. So
(∀y)(∃x)Ryx is equivalent to (∀y)[ (∃x)Ryx ]
or with three quantifiers,
(∃z)(∀y)(∃x)Qzyx is equivalent to (∃z){ (∀y)[ (∃x)Qzyx ] }