How does the change in heat equal work done? In a numerical my teacher said that delta Q = W. How?

According to the first law of thermodynamics, heat, internal energy and work are related by the following expression:

Change in internal energy = heat added to the system - work done

or `DeltaU`  = `DeltaQ` - W

where W represents the work done by the system. 

In simple terms, when heat is added to a system, the internal energy of the system changes and/or it does some work. 

There can be cases where the internal energy is conserved and cannot be changed. In such cases, 

delta Q = W

That is, the change in heat is equal to work done by the system, since change in internal energy is zero. In other words, if we add heat to such a system, it will do work. On the other hand, if the system does work, it loses heat. 

An example of such a system is an ideal gas in an isothermal process (temperature is constant). In such a system, the change in internal energy would be zero and the change in heat will be equal to the work.

Hope this helps.