To find out how many kilograms of paper Jackson's office will recycle after 4 weeks, we first determine the recycling rate per week.
Given that Jackson's office recycled a total of 24 kilograms of paper over 2 weeks, we can calculate the unit rate (the amount recycled per week) as follows:
\[ \text{Unit rate} = \frac{\text{Total recycled}}{\text{Number of weeks}} = \frac{24 \text{ kg}}{2 \text{ weeks}} = 12 \text{ kg/week} \]
Now, to find out how much will be recycled over 4 weeks, we multiply the unit rate by the number of weeks:
\[ \text{Total recycled after 4 weeks} = \text{Unit rate} \times \text{Number of weeks} = 12 \text{ kg/week} \times 4 \text{ weeks} = 48 \text{ kg} \]
Thus, after 4 weeks, Jackson's office will have recycled:
\[ \boxed{48} \text{ kilograms} \]