C = 684 - H

2/3H = 3/5C = 3/5(684-H)

Solve for H, then C.

The bot's answer again makes no sense

C = 684 - H
H = 684 - C

actual numerical answers are not possible from the data given

Unless 2/3H = 3/5C is part of the question, then
10H = 9C
H = (9/10)C and C = (10/9)H

C = 684 - H
C = 684 - (9/10)C
(1 9/10)C = 684
C = 360

H = (9/10)360
= 324

H = 408

C = 276