Elmo bakes cookies at a rate of one per 5 minutes. Big Bird bakes cookies at a rate of one per 6 minutes. Cookie Monster [i]consumes[/i] cookies at a rate of one per 4 minutes. Together Elmo, Big Bird, Cookie Monster, and Oscar the Grouch produce cookies at a net rate of one per 8 minutes. How many minutes does it take Oscar the Grouch to bake one cookie?
1. Let's denote the rates of baking and consuming cookies as follows:
   - Elmo's rate: $\frac{1}{5}$ cookies per minute
   - Big Bird's rate: $\frac{1}{6}$ cookies per minute
   - Cookie Monster's rate: $-\frac{1}{4}$ cookies per minute (since he consumes cookies)
   - Oscar the Grouch's rate: $\frac{1}{o}$ cookies per minute

2. According to the problem, the net rate of producing cookies by all four together is $\frac{1}{8}$ cookies per minute. Therefore, we can set up the equation:
   \[
   \frac{1}{5} + \frac{1}{6} + \frac{1}{o} - \frac{1}{4} = \frac{1}{8}
   \]

3. To solve this equation, we first find a common denominator for the fractions on the left-hand side. The least common multiple of 5, 6, 4, and 8 is 120. We rewrite each fraction with this common denominator:
   \[
   \frac{1}{5} = \frac{24}{120}, \quad \frac{1}{6} = \frac{20}{120}, \quad \frac{1}{4} = \frac{30}{120}, \quad \frac{1}{8} = \frac{15}{120}
   \]

4. Substituting these values into the equation, we get:
   \[
   \frac{24}{120} + \frac{20}{120} + \frac{1}{o} - \frac{30}{120} = \frac{15}{120}
   \]

5. Combine the fractions on the left-hand side:
   \[
   \frac{24 + 20 - 30}{120} + \frac{1}{o} = \frac{15}{120}
   \]
   \[
   \frac{14}{120} + \frac{1}{o} = \frac{15}{120}
   \]

6. Isolate $\frac{1}{o}$ by subtracting $\frac{14}{120}$ from both sides:
   \[
   \frac{1}{o} = \frac{15}{120} - \frac{14}{120}
   \]
   \[
   \frac{1}{o} = \frac{1}{120}
   \]

7. Taking the reciprocal of both sides, we find:
   \[
   o = 120
   \]

The final answer is $\boxed{120}$