Multiples of 3 or 4 are: 3,4,6,8,9,12

the total number of roll results is 6*6 = 36

let p(x) is the probability that the sum is x then we have

for x = 3 since 1 + 2 = 3, 2 + 1 = 3 so there are 2 events when the sum is 3 and we can write

p(3) = 2/36

for x = 4 since 1 + 3 = 4, 3 + 1 = 4, 2 + 2 = 4 so there are 3 events when the sum is 4 and we can write

p(4) = 3/36

for x = 6 since 1 + 5 = 6, 5 + 1 = 6, 2 + 4 = 6, 4 + 2 = 6, 3 + 3 = 6 so there are 5 events when the sum is 6 and we can write

p(6) = 5/36

for x = 8 since 2 + 6 = 8, 6 + 2 = 8, 3 + 5 = 8, 5 + 2 = 8, 4 + 4 = 8 so there are 5 events when the sum is 8 and we can write

p(8) = 5/36

for x = 9 since 3 + 6 = 9, 6 + 3 = 9, 4 + 5 = 9, 5 + 4 = 9 so there are 5 events when the sum is 9 and we can write

p(9) =4/36

for x = 12 since 6 + 6 = 12 there is 1 event when the sum is 12 and we can write

p(12) = 1/36

P(3,4,6,8,9,12) = 2/36+3/36+5/36+5/36+4/36+1/36 =20/36 = 5/9

the probability is 5/9 or 55.6%.