Your company has a highly available Direct Connect solution that utilizes two datacenters. Each data center contains one two-connection LAG and one standard DX connection. How many LOAs will be filled out in total if your company completes an order to add a new connection to each one of the LAGs?

Answer options:

A.1
B.4
C.6
D.10

Answer – B
AWS documentation and LOA is used for DX, interconnect and Link Aggregation Group
https://docs.aws.amazon.com/cli/latest/reference/directconnect/describe-loa.html
So in this example each data centre would have 2 LOAs (1 DX and 1 LAG) = 4 and adding more connection to the LAGs will not increase the number of LOAs.
The AWS documentation mentions the following on link aggregation group 
When you create a LAG, you can download the Letter of Authorization and Connecting Facility Assignment (LOA-CFA) for each new physical connection individually from the AWS Direct Connect console
For more information on link aggregation group , please refer to the below link
http://docs.aws.amazon.com/directconnect/latest/UserGuide/lags.html