dat<-data.frame(
ID=c(100,101,101,101,102,103),
DEGREE=c("BA","BA","MS","PHD","BA","BA"),
YEAR=c(1980,1990, 1992, 1996, 2000, 2004))

> dat
ID DEGREE YEAR
100     BA 1980
101     BA 1990
101     MS 1992
101    PHD 1996
102     BA 2000
103     BA 2004

ID DEGREE_1 DEGREE_2 DEGREE_3 YEAR_DEGREE_1 YEAR_DEGREE_2 YEAR_DEGREE_3
 100    BA                           1980
 101    BA      MS      PHD          1990        1992          1996
 102    BA                           2000
 103    BA                           2004

dat$DEGREE<-as.character(dat$DEGREE)
dat %>% group_by(ID) %>%
mutate(DegreeNum = paste("Degree", row_number(), sep = "_"))%>%
mutate(DegreeYear = paste("YearDegree", row_number(), sep = "_"))%>%
spread(DegreeNum, DEGREE, fill = "")%>%
spread(DegreeYear,YEAR,fill="")%>%
as.data.frame()

 ID Degree_1 Degree_2 Degree_3 YearDegree_1 YearDegree_2 YearDegree_3
 100   BA                           1980
 101                    PHD                                  1996
 101            MS                               1992
 101   BA                           1990
 102   BA                           2000
 103   BA                           2004