Operation Mountain Fury

Operation Mountain Fury was a NATO-led operation begun on September 16, 2006 as a follow-up operation to Operation Medusa, to clear Taliban rebels from the eastern provinces of Afghanistan. Another focus of the operation was to enable reconstruction projects such as schools, health-care facilities, and courthouses to take place in the targeted provinces.
During the operation, the Taliban suffered large losses during direct battle with NATO coalition forces; as a result, they are expected to focus more on tactics such as the use of Improvised Explosive Devices, according to sources such as NATO's top commander James L. Jones and Canadian defence minister Gordon O'Connor. Jones also linked the large-scale production of opium to increased insurgent violence.
The Canadians continue fighting in Panjwaii.
The Canadian forces began reconstruction efforts after major combat operations of Operation Medusa had ceased. But they still encountered fierce fighting. Canadian Forces began the construction of a road, code-named "Summit", from the Panjwaii area to outlying areas including Kandahar city. But the Taliban continued to attack them both in Panjwaii and in Kandahar city with ambushes, IED attacks or suicide bombings taking the lives of Canadian soldiers along with some Americans. The Canadian involvement in operation Mountain Fury was stepped up when they mounted an operation of their own called Operation Falcon's Summit on December 15, 2006. 
During Falcon Summit, the Canadians gained control of several key villages and towns that were former Taliban havens, such as Howz-E Madad. During the first week of the operation, massive Canadian artillery and tank barrages were carried out in a successful attempt to clear pockets of Taliban resistance.
The Americans go on the offensive.
Meanwhile, the Americans began their combat operations against the Taliban forces that were entrenched in the mountains on the border with Pakistan in the east in the provinces of Paktika, Khost, Ghazni, Paktia, Logar and Nuristan. The 10th Mountain Division led the charge establishing many remote outposts in regions that were previously Taliban dominated. These outposts came almost under continued attacks as well as did the American combat patrols which resulted in almost 150 casualties inflicted on the Americans in two and a half months by the beginning of December.
The British attack repelled.
On December 5, 2006 the British Marines attacked a Taliban-held valley in southern Afghanistan near Garmsir but withdrew after a ferocious counterattack that withstood air strikes and artillery fire. Scores of soldiers ran across a bridge over the Helmand River under a full moon shortly before daybreak and began sweeping south through wheatfields in the south of the province, the opium center of the world's major producer. Marines initially faced only sporadic resistance but when they advanced, Taliban fighters launched a ferocious, organized riposte with heavy weapons and tried to outflank the British troops. The Taliban withstood barrages of air strikes from AH-64 Apache helicopters, 500 pound bombs dropped by B-1 bombers and withering cannon fire from A-10 ground attack jets before the British finally withdrew after a 10-hour battle. The Taliban fighters, who say they have the expertise to defeat the strongest army, had dug sophisticated networks of trenches often leading from compound to compound. The assault was the latest in a series of battles by British forces around the bridgehead and the short road at the north end of the valley, criss-crossed by networks of ancient canals that make Helmand fertile enough to produce a third of the world's opium crop. The British said they considered the assault a success as they had cleared out areas near the "D.C.," a tiny strip of road and ruined buildings on the eastern side of the Helmand River. But without more Afghan troops to hold the ground there was little hope of doing much more.
Mullah Osmani Killed.
On December 19, 2006 a NATO air strike targeting a car in a deserted area of Helmand province killed Mullah Akhtar Mohammad Osmani along with two other men. He was the top Taliban commander for all of their operations in southern Afghanistan.
The British attack again.
The next month, an operation called Operation Clay was launched on New Year's Day. Plymouth-based 42 Commando were engaged in four days of fighting. The British had running firefights for up to four days against fairly coherent sustained attacks of small arms, rockets and indirect fire. About 110 Royal Marines carried out the operation in northern Helmand. During the operation British troops destroyed a Taliban training camp and killed dozens of insurgents, according to the military.
From the 13th to the 15th of January, 2007 Royal Marines fought Taliban forces in the south of Helmand, attacking their positions and a major base. During the fighting one Royal Marine was killed and several were wounded. The Taliban suffered at least 30 killed.