A question about cancel in Magic the Gathering.?

The spell cancel, is a counterspell. It works very simply, if a spell is upon the stack at a given time, you can recieve priority to cast, and decide to cast cancel thereby countering/negating/removing the spell from the stack prior to its resolving.

However, an equipment is only a spell when it is on the stack (the stack is a place where spells go prior to coming onto the field, usually only for a few seconds at most, to allow other players to play something first if they so choose such as counter magic) If that particular piece of equipment has been on the field for a while it is no longer a spell and can no longer be countered, the ability of equipping a creature, is an ability and not a spell, there are a few things that can counter abilities on the stack but cancel is not one of them.

A spell is basically when a card is being played while its in stack, everything is a spell except lands.
Cards already on the field are not spells, so no

You could only if they're using a spell to attach the equipment.

There are some of those, but otherwise, no:

702.6. Equip

702.6a Equip is an activated ability of Equipment cards. "Equip [cost]" means "[Cost]: Attach this permanent to target creature you control. Activate this ability only any time you could cast a sorcery."

702.6b For more information about Equipment, see rule 301, "Artifacts."

702.6c If a permanent has multiple instances of equip, any of its equip abilities may be activated.

A spell is a card (or a copy of a card) that is played from the hand (normally but can be played from elsewhere) by paying its mana cost, choosing targets, choosing modes, paying other costs, and moving it to the stack. It is on the stack where it can be countered by something like Cancel. An ability like the equip ability uses the stack so can be responded to but is not a spell because it does not have a converted mana cost but a cost to activate the ability. Converted mana costs are always what is in the top right hand corner of the card.