try to use this code $query->where([ ['start_date', '<=' Carbon::today()->format('Y-m-d')] , ['end_date', '>=' Carbon::today()->format('Y-m-d')] ]);

you must add , to the code

You should try this:

public function searchresult (Request $request){

$keyword = $request->name;
$search = Mosque::where('name', 'LIKE',"%{$keyword}%" )
    ->whereHas('events', function($query) {
        $query->where([
            ['start_date', '<=',Carbon::today()->format('Y-m-d')],
            ['end_date', '>=' ,Carbon::today()->format('Y-m-d')]
        ]);
    })
    ->orWherehas('activities', function($query) {
        $query->where([
            ['start_date', '<=',Carbon::today()->format('Y-m-d')],
            ['end_date', '>=',Carbon::today()->format('Y-m-d')]
        ]);
    })
    ->get();
}