Shawn:
During the civil war, the lack of familarity caused much confusion which led to artillery pieces being wrongly identified. An example is the 2.9" and 3" Parrott rifles referred to as a 10 pounder rifle. They are correctly known as 3" rifles as all rifles were referred to by diameter size. Smoothbore cannon were called pounders based on the weight of a solid shot fired by the gun. Another famous example is the Napoleon cannon, called so by it was based on a earlier french design. Some say it is a howitzer while others say it is a gun. The official nomenclature is as a 12 pounder light gun. The Napoleon bronze tube weighted 1,280 pounds while the 12 pounder field gun bronze tube weighted up to 1,800 pounds, so you see there was a difference.

Lack of familarity caused the misidentifing of artillery pieces and continues to do so today.

There was never a 6 pounder howitzer because a gun of this size would have been to small, of such short range to have any effective results. There was reports of a 6 pounder British Whitworth rifle but none has survived the war and time. These were rare and not a howitzer as you asked about so don't confuse the two.

In short, NEVER a 6 pounder howitzer.
Ron