This is the 7284th most frequent Russian word.
всеобщая
Universal.
In this sentence, 'всеобщей' describes harmony and understanding as being universal, emphasizing inclusivity and application to all groups.
Она мечтала о всеобщей гармонии и понимании.
She dreamed of universal harmony and understanding.
Here, 'всеобщие' is used to portray ecological problems as being common and significant to everyone.
На конференции обсуждали всеобщие проблемы экологии.
The conference discussed universal ecological problems.
In this context, 'всеобщую' refers to love and respect being experienced or given unexceptionally by everyone.