Let p be the number of parts of peat moss she has to add.
Initially we have (peat moss)/sand=3/4, so we have 7 parts in the whole mixture, 3/7 of peat and 4/7 of sand. In the final mixture 60% is peat moss and therefore 40% is sand.
Now we add p parts of peat moss so the whole mixture contains 7+p parts, consisting of 3+p parts of peat moss but 4 parts of sand. So we have (3+p)/4=60/40=3/2.
Cross-multiply: 2(3+p)=12, 6+2p=12, 2p=12-6=6, p=3. She has to add 3 parts of peat moss.
CHECK
Now the mixture has 3+3=6 parts of peat moss and still 4 parts of sand. Total parts in the mixture = 6+4=10, of which 6/10 are peat moss (60%) and 4/10 (40%) are sand.