Holes in drywall slightly too wide for screws
Putting screws directly into drywall, particularly the type shown in your photo, will rarely (if ever) work. The drywall is not strong or firm enough to hold screws without hollow-wall anchors of some sort.

You need to tell us more, however; if you want advice as to what sort of anchoring system you need. What is the reason you need to put screws in the wall?