A promotional method frequently used by hamburger restaurants is to redeem a section of a print advertisement, referred to as a:

The correct choice is the coupon, as it specifically refers to a printed advertisement section that customers can redeem for discounts or special offers on products. Coupons are a well-established marketing strategy used by quick-serve restaurants, particularly hamburger chains, to incentivize customers to visit their location, try new items, or make a purchase they might not have otherwise made.

This method effectively attracts customers by providing a tangible benefit that encourages them to engage with the brand or menu offerings. Coupons can also create urgency if they have expiration dates or limited-time offers, further driving traffic and sales.

The other options represent different promotional strategies but do not specifically refer to this practice. For instance, vouchers usually imply a broader use for various transactions or services, discount cards typically offer ongoing discounts rather than specific redemption from an advertisement, and promotional offers can encompass a variety of marketing tactics without the specificity of a coupon being a print element. Thus, the coupon is the most accurate term for the action described in the question.