How does LEED encourage the use of locally sourced materials?

The choice highlighting the awarding of points for materials extracted nearby is the correct answer because LEED (Leadership in Energy and Environmental Design) specifically encourages the use of locally sourced materials as a way to reduce the environmental impact of transportation and to support regional economies. By providing points for materials that are sourced within a certain radius of the project site, LEED promotes sustainable practices that not only lessen carbon emissions associated with long-distance transportation but also contribute to the local economy by using materials from nearby manufacturers and suppliers. This approach supports community wellbeing and fosters regional skill development, as well as reducing the life cycle impacts of materials used in construction.

The other options lack the specific relationship to the LEED system's focus on sustainable sourcing. Flexible project deadlines do not directly incentivize local sourcing, financial incentives are not a standard part of the LEED framework for sourcing decisions, and promoting global sourcing counters the intent of supporting local economies and minimizing transportation environmental impact.