Without more context, it might be open to other interpretations, but here's an attempt to characterize the phrases in the scope of Western philosophy of mind. In a general sense, I would say that the Subject of Knowledge is the philosophical notion of agent, and the Object of Knowledge it the what the agent is about, the subject of intentionality usually taken to be a representation and together they form a system where one cannot exist without the other.
To hear is to hear something.
A person engaged in the action of hearing is thus about auditory experiences perhaps taken as sense data or qualia of sound.
To be angry is to be angry about something.
A person in a state of anger is thus there because of a response in regards to being about some idea that triggers anger.
Thinking is thinking about something.
For an agent to be processing thoughts requires thoughts which are about something.
In the Western canon going back to Plato, a strong thread of philosophical realism runs through the thinking that attempts to efface the thinker and divide the thinker from the thought. On this way, truth is not a construction of the mind, but an objective and real thing independent of thought itself. That belief was strong that it carried from Ancient Greece to the logical positivists in the 20th century who attempted to show that scientific realism entailed universal objectivity about ontological matters by way of the objective observation.
Instead, they ran into theory-ladenness and underdetermination which strongly suggests that any "objective" thing is actually a product of normativity at some level. There is no absolute and clear line, in the words of Hume, between Is and Ought. Buddhism, particularly Chan and Zen flavors, attack that belief relentlessly.