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Pay very close attention to the order of the letters in △ABC ~ △DBE.
The ordering tells us how the letters pair up.
A and D are the 1st letters of ABC and DBE respectively
B and B are the 2nd letters of ABC and DBE respectively
C and E are the 3rd letters of ABC and DBE respectively
From there we know that
AC pairs with DE because both involve the 1st and 3rd letters
CB pairs with EB because both involve the 3rd and 2nd letters
Now we can set up a proportion, cross multiply and solve for EB,
AC/DE = CB/EB
6/4 = 5/EB
6*EB = 4*5
6*EB = 20
EB = 20/6
EB = (10*2)/(3*2)
EB = 10/3
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