PLEASE HELP! How do I solve this problem?

The toughest part of this problem could be deciding what names to give the quantities of one-Euro and two-Euro coins.

-- I called the number of one-Euro coins ' N '.
Each of them is worth 1 Euro, so all ' N ' of them are worth ' N ' Euros.

-- I called the number of two-Euro coins ' T '.
Each of them is worth 2 Euros, so all ' T ' of them are worth ' 2T ' Euros.

-- The total number of coins in Penny's pocket is (N + T), and it says there are 11.

-- Their total value is (N + 2T), and it says the total value is 18.

So now you have two equations, with two unknowns.

               N + 2T  =  18
               N +  T  =  11

Subtract the bottom equation from the top one, and you get:

          (N - N) + (2T - T)  =  (18 - 11)

                             T        =      7         (there are 7 two-Euro coins in her pocket)

That right there is the answer to the question, so you don't need to go
any farther.  But if you wanted to, you could also figure out how many
one-Euro coins there are in her pocket.