Will my laptop run the Sims 4 ?

@LILLIBU2  Yes, you can easily play Sims 4 on this laptop.  It should be able to run the game on medium-high or high graphics settings even if you install every pack.

I'm not sure how the game would have ruined your previous laptops, but a $200 computer isn't really equipped to be running Sims 4 in the first place.  In general, the only reasons why an otherwise capable laptop would be damaged by running Sims 4 are if it's allowed to overheat or if it has a hardware defect.  For the first, make sure it can cool itself properly: play on a hard flat surface, or use a laptop tray or similar to elevate it so air can flow underneath.  For the second, that's why laptops come with a warranty.