Design the circuit such that the output voltage is 2.4V
First off, this is a horrible way to design a circuit to have a fixed output voltage. You would never do this in the real world. But I'll assume it's a homework problem and it's meant to test your knowledge of diode behavior. 

The key is to remember the Shockley diode equation

$$I = I_s\ \exp(\frac{qV}{nRT}-1)$$

You know one point on the characteristic curve (V=0.7 V when I=1 mA), but there are two unknown parameters to describe the diode: \$I_s\$ and \$n\$. You'll have to assume you know one of them close enough and then use the equation to get the other one. n is more likely to be close to a "typical" value, so I'd choose \$n=1\$ (If you've been given SPICE models for any "typical" diodes in class, then use the n values from one of those models instead of just n=1) and then find \$I_s\$ to match the given datapoint. 

Once you have \$I_s\$ then you have to find the \$I\$ that gives you 0.8 V per diode in order to get 2.4 V at the output. 

But again, you'd never design a circuit this way in reality. If the load on the output draws more than microamps it's going to change the output voltage by more than you want (given that the person who designed the problem seems to care about the difference between 2.1 and 2.4 V output)