Using tidyr and using some created data since I didn't want to get the data from your pictures:
> data
  year      net    ceded
1    1 266.73007 317.6823
2    2 729.50176 366.0213
3    3 425.06088 162.0960
4    4 723.09221 348.2421
5    5  45.05688 467.0686
6    6  44.78075 154.3635
7    7  59.73864 750.4060
8    8 526.06015 585.1687
9    9 229.78809 554.1722
10  10 355.92545 232.5220
Now we want to transform those data into a "longer" format:
data %>%
  pivot_longer(cols=c(net, ceded), names_to="id", values_to="amount")
yields
# A tibble: 20 x 3
    year id    amount
   <int> <chr>  <dbl>
 1     1 net    267. 
 2     1 ceded  318. 
 3     2 net    730. 
 4     2 ceded  366. 
 5     3 net    425. 
 6     3 ceded  162. 
 7     4 net    723. 
 8     4 ceded  348. 
 9     5 net     45.1
10     5 ceded  467. 
11     6 net     44.8
12     6 ceded  154. 
13     7 net     59.7
14     7 ceded  750. 
15     8 net    526. 
16     8 ceded  585. 
17     9 net    230. 
18     9 ceded  554. 
19    10 net    356. 
20    10 ceded  233. 
An alternative using reshape2:
data %>%
  melt(id.vars=c("year"), measure.vars=c("net", "ceded"))