This repeatedly happens to me as I try to play the game I have repaired,update,remove and all that jazz and nothing has changed.I really love Sims 4 and it hurt I have to stop playing the game due to my progress being lost if I exit out the game.
From your screenshot it looks like it's not letting you go to manage worlds to save. Have you tried just saving from the menu?
If it is stuck loading the game, do your sims have any actions qued? There might be conflicting actions, so you could maybe confirm this from trying to save with another household.
What platform are you running the game on? PC, Mac or one of the consoles?
And is the game in your pic in build mode or live mode? And as @LKM747 suggested, does it do the same thing when you save with the Game Options menu?
Hope this helps.
