To round a number, you take the number to the right of where you want the number to be accurate to. In this problem the second decimal place is #color(red)(3)#:
#7.8color(red)(3)65#
The number to the right of it is #color(blue)(6)#:
#7.8color(red)(3)color(blue)(6)5#
If the number to the right is greater than or equal to #5# you add 1 to the number and eliminate all of the other numbers to the right.
If the number to the right is less than #5# you leave the number as is and eliminate all of the other numbers to the right.
In this case #color(blue)(6)# is greater than or equal to #5# so we need to add #1# to #color(red)(3)# and eliminate all the other numbers to the right:
#7.8color(red)(3)color(blue)(6)5# accurate to the second decimal place is #7.8color(red)(4)#