Since $60$ particles are emitted every minute and there are $60$ minutes in one hour, there are $60\cdot60=3600$ particles emitted in one hour.
(a) If the usual rate of emission was increased by a factor of $60$, then there would be $60\cdot60=3600$ particles emitted every minute. Thus $3600\cdot60=216,000$ particles emitted in one hour.
(b) If it is increased by $25$% we will have $75$ particles emitted every minute. This is so because $25$% of $60$ is $15$. Thus $75\cdot60=4500$ particles emitted in one hour.
(c) If it is decreased by $75%$, then we have only $15$ particles emitted every minute. Thus $15\cdot60=900$ particles emitted in one hour.
(d) If it is increased by 200% we will have 180 particles emitted every minute. Thus 180*60=10800 particles emitted every hour.
(e) If the usual amount was decreased by 100%, then there would be zero particles emitted.