Why is the water (either hot or cold) in the kitchen suddenly shutting off
Start by shutting off the water supply for the Hot and Cold lines under the sink.
Next detach (unscrew) the hot supply line from the faucet line (if possible). If you can't than unscrew the hose from the valve.
Place a bucket under the valve and a rag over the open connection. Slowly open the valve to check for water flow. When (and if) water is flowing into the bucket open the valve more to jettison any debris in the line. Do the same for other side.
If no water is present at the valve than the problem is before the valve. When you reconnect the faucet hose after confirming water is flowing but no water flows from the faucet thr problem is after the valve.