The White House, meanwhile, has set up its own interagency

Hi farhanc85

I'm glad to help.

The White House, meanwhile, has set up its own interagency panel that would look at how to protect consumers while also make United States companies more competitive internationally

A. that would look at how to protect consumers while also make
B. that will look at the protection of consumers while also making
C. for looking at how to protect consumers while also making
D. that will look at how to protect consumers while also making ==> CORRECT
E. for looking at protecting consumers and also making

First split: "make" VS "making"
After "while" you have two options:
(1) "while" is subordinating conjunction, thus after "while" you must use a complete sentence. "While also make...." is short of subject, so this part cannot be a complete sentence. ==> A is out.
(2) if the part after while has the same subject, you can use "while + V-ing". For example: he does his job while talking on the phone.
B, C, D, E which say "while also making" ==> remain.

Second split: "that" vs "for"
"For" is incorrect preposition, the intended meaning is about the "plan" - the White house has set up a panel to look at...... Thus, "for" which means "because" is incorrect. ==> C, E are out.
"That" is correct modifier. B, D remain.

Third split: "look at the protection" vs "look at how to protect".
Clearly, the intended meaning is about the "plan" of the White house to protect consumers. The white house does not look at "the protection OF customers". B changes meaning.

Only D left. ==> CORRECT.

Hope it's clear.