let f(x)=−3x
the graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 and a translation of 4 units right.
what is an equation for g(x)?

For a translation of 4 units right, the graph will become -3(x-4). the 4 is negative to indicate that the translation is right.
For a vertical stretch of 4, the graph will become 4x-3(x-4)=-12(x-4). 

With this information, g(x)=-12(x-4)