Both ellipses have e=4/5.
For E1 (a>b):
b2=a2(1−e2)=9a2/25.
Latus rectum l1=2b2/a=18a/25.
Distance between foci of E1:
2ae=8a/5=8⇒a=5, so l1=18/5.
For E2 (A<B, major axis along y):
A2=B2(1−e2)=9B2/25.
Latus rectum l2=2A2/B=18B/25.
Given 2l12=9l2:
2⋅25324=9⋅2518B⇒648=162B⇒B=4.
Distance between foci of E2=2Be=2⋅4⋅54=532