The most valuable New Zealand Sixpence would be the 1957 "Strapless" coin.
Not all 1957 Sixpences were strapless, but about 200,000 of the 2.4 million minted show Queen Elizabeth with a bare right shoulder, ie. no garment strap.
Second would be the 1941 and 1942 Sixpences.
All years of issue of the New Zealand Sixpence from 1933 to 1965 featured the now extinct "huia", a species of wattlebird.
There are no rare general circulation New Zealand Sixpences. In all years they were minted, the minimum quantity minted was 360,000. The 1957 "Strapless" Sixpence of which there were 200,000 minted, is quite valuable in mint condition. What might be considered rare are the Proof Sixpences. In most years they were minted, there were 200 or less minted. The rarest of these would be the 1965 Proof Sixpence of which there were 10 minted.
There were no New Zealand Sixpences minted prior to 1933.
"Zack" was a slang term used mostly in Australia and New Zealand for a Sixpence. The term is thought to have originated with the Scottish pronunciation of Sixpence - being "Saxpence", with a thick Scottish accent.
The Huia featured on the reverse of all New Zealand Sixpences from 1933 to 1965 inclusive.
New Zealand Sixpences from 1947 to 1965 were made from a copper nickel alloy.
What were New Zealand and Australia for the British
See the links to the related questions below.
The Sixpence (six pennies) came from the British currency and spread to many of the Commonwealth countries at different times. Since all countries have now decimalised, the Sixpence is no longer in use. Apart from Britain, there was Australia, New Zealand, Fiji, South Africa, Rhodesia, Malta and many others.
Valuable Trading Post
All New Zealand "silver" coins from 1933 to 1946 inclusive had a 50% silver content. All New Zealand "silver" coins from 1947 onwards, were made from a copper/nickel alloy.
You do not specify a country. As far as coins are concerned, the terms "rare" and "valuable" are not the same thing and do not necessarily go hand in hand. There are no 1956 Australian, British or New Zealand coins that could be considered to be rare. Variants of the 1956 New Zealand Penny and Threepence are valuable. About 50,000 Pennies of a total of 3.6 million minted and 300,000 Threepences of a total of 4.8 million minted, were struck showing Queen Elizabeth II with a bare shoulder. These are referred to as the "strapless" coins. There was a similar "strapless" Sixpence minted in 1957. The greatest value is associated with mint uncirculated coins or coins in excellent condition.