u is an unknown function. You don't need to know explicitly what it is (so long as it's smooth enough to be twice differentiable).

This is an exercise in using the chain rule. Start with . Differentiate this again, partially with respect to s, using the chain rule again, together with the product rule, to get an expression for in terms of , and .

Then do the same procedure, differentiating twice partially with respect to t this time, to get an expression for . Add the two expressions together and hope that the terms cancel out to give the result that you want.