The line came from Eren in Chapter 139 of the Attack on Titan (AOT) manga. In the panel he revealed his selfish desire of not wanting Mikasa to find another man and moving on after his death. The revelation was rather pathetic and out of character for him that many AOT fans made memes and turned his ’10 years at least’ line into a copypasta.
No, I don't want that! Mikasa finding another man?! I want her to think about me and no one else for the rest of her life. Even After I die...I want to be at the front of her mind for a while! Ten years, at least!!I don't want to die...I want to be with Mikasa. With everyone else...No. No, I don't want that! Mikasa finding another man...?! I want her to think about me and no one else for the rest of my life! Even after I die... I want to be at the front of her mind for a while! Ten years, at least!! ...Please don't repeat that to Mikasa... I want her to be happy... I really do. But... AGH... YEAH... DAMMIT... ...I don't wanna die. I want to be with Mikasa... with Everyone.