I'm assuming that \(\displaystyle H\) is a Hilbert space, although it doesn't say this in the question. I'm really not sure where to start with this. All I have is that since \(\displaystyle S,T\) are bounded there adjoints \(\displaystyle S^*\) and \(\displaystyle T^*\) exist and that:

\(\displaystyle <Tx,y>=<x,T^*y>\) for all \(\displaystyle x\in H\),\(\displaystyle y\in H\)