1. The problem asks to find the total number of items delivered when a coach orders $4m$ boxes, each containing $2y+7$ items. 2. The expression to find the total items is given by multiplying the number of boxes by the number of items per box: $$4m(2y+7)$$ 3. Use the distributive property to expand the expression: $$4m \times 2y + 4m \times 7$$ 4. Multiply the terms: $$8my + 28m$$ 5. Therefore, the total number of items delivered is $$8my + 28m$$. 6. Among the given options, the correct answer is: $$8my + 28m$$.