When you insert this product management slip into this time stamp machine, the date and time will be stamped on it.
Literal
This product-management-slip [obj-を] this time-stamp [to-に] insert-[conditional-と] date [and-と] time [subj-が] stamped [passive-されます].
商品管理伝票 is a four-compound string: 商品 'product' + 管理 'management' + 伝票 'slip/voucher.' 打刻 'stamping' (打 'strike' + 刻 'engrave') is the technical term for time-stamping. The conditional と marks the automatic, mechanical consequence: 'when you insert, (it automatically) stamps.'