The Open Defence to the Ruy Lopez, a favourite of World Champions Euwe and Anand. I read in a Jon Speelman column once that this defence was now thought to be slightly suspect at the very top level but I like it because you get plenty of elbow room.
6. Rf1e1
This move regains the pawn immediately. It's fine but gives fewer chances for white to secure an opening advantage. Stronger is 6. d4 which threatens to win the pawn back in a more complicated fashion. Because 6...exd4 is the very risky Riga Variation, black normally plays 6...b5 7. Bb3 d5 8. dxe5 Be6.
Up to here the moves have been logical and quite common. With White's last move the process to recover the pawn has been completed, Black has blocked the e file ready to castle. White must now make a decision about how he wants to develop his pieces, particularly those on the queen-side over the next few moves. The problem with moves like Qf3 is that the one move mate threat is easily defended by the move Black was going to play anyway. Also the central strike on the knight with d4 is no longer available as the Queen's protection has been lost and it is not easy to find follow ups that can force the pace sufficient to gain any advantage in space, structure or material. A slower build up is required developing the remaining pieces to useful squares.
9... O-O 10. d3
White's central influence is reduced compared to playing d4 on the previous move.
10... Bc8e6
This move reinforces the protection of f7 in case Qg3 and Bh6 requires Re8 (unprotecting f7) and g6. If the loose knight on c5 is attacked then it can retreat to d7 if necessary to challenge White's central knight.
11. Qf3g3
I think this wastes a development tempo as once again the threat of Bh6 is easy to counter. Black can play Re8 and g6 or Bf6 protecting the g7 square at the same time increasing the influence of those pieces on other parts of the board. Get the pieces out!
11... Be7f6
Now the square b2 comes under focus as well as the protection of g7.
12. Bc1h6
Again there doesn't seem to be an obvious way to develop the attack beyond this move and so the bishop is likely to have to move again very soon which constitutes a further waste of time. Nc3 then Bf4 (looking at c7) might have been better.
12... Rf8e8
Now g6 is available to black at no material cost.
13. Ne5f3
The knight moves again and I was unable to see where you intended to play it. The move uncovers the dark squared bishop's attack on the b2 pawn and should have lead to immediate material disadvantage.