I haven't played this game. I'm assuming you're not getting a button prompt or something to actually set off the explosion? I looked around online, but there aren't many guides available for this game.

Check out the IGN Game Guide at http://guides.ign.com/guides/849458/page_3.html
All it mentions about this specific mission is:
"Objective: Set C4 charges to destroy bridge and secure LZ.

Have your squad kick open the gate in the corner and fight your way across the bridge while you order your squad to set the C4 charges. The first charge is on the right, with the second on the left. Cross the bridge and take over the turret in the tower, then shoot the troops that emerge until the C4 is detonated."

Usually, you would send your squad to set the charge and set off the explosion. Not sure how it works in multiplayer. Hope that helps some.
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