I would be tempted to use grepl, which should give all the lines with matches and can be generalised for arbitrary strings.
mydata_2 <- read.table(textConnection("
sex age height_seca1 height_chad1 height_DL weight_alog1
1 F 19 1800 1797 180 70.0
2 F 19 1682 1670 167 69.0
3 F 21 1765 1765 178 80.0
4 F 21 1829 1833 181 74.0
5 F 21 1706 1705 170 103.0
6 F 18 1607 1606 160 76.0
7 F 19 1578 1576 156 50.0
8 F 19 1577 1575 156 61.0
9 F 21 1666 1665 166 52.0
10 F 17 1710 1716 172 65.0
11 F 28 1616 1619 161 65.5
12 F 22 1648 1644 165 57.5
13 F 19 1569 1570 155 55.0
14 F 19 1779 1777 177 55.0
15 M 18 1773 1772 179 70.0
16 M 18 1816 1809 181 81.0
17 M 19 1766 1765 178 77.0
18 M 19 1745 1741 174 76.0
19 M 18 1716 1714 170 71.0
20 M 21 1785 1783 179 64.0
21 M 19 1850 1854 185 71.0
22 M 31 1875 1880 188 95.0
23 M 26 1877 1877 186 105.5
24 M 19 1836 1837 185 100.0
25 M 18 1825 1823 182 85.0
26 M 19 1755 1754 174 79.0
27 M 26 1658 1658 165 69.0
28 M 20 1816 1818 183 84.0
29 M 18 1755 1755 175 67.0"),
sep = " ", header = TRUE)
which(grepl(1578, mydata_2$height_seca1))
The output is:
> which(grepl(1578, mydata_2$height_seca1))
[1] 7
>
[Edit] However, as pointed out in the comments, this will capture much more than the string 1578 (e.g. it also matches for 21578 etc) and thus should be used only if you are certain that you the length of the values you are searching will not be larger than the four characters or digits shown here.
And subsetting as per the other answer also works fine:
mydata_2[mydata_2$height_seca1 == 1578, ]
sex age height_seca1 height_chad1 height_DL weight_alog1
7 F 19 1578 1576 156 50
>
If you're looking for several different values, you could put them in a vector and then use the %in% operator:
look.for <- c(1578, 1658, 1616)
> mydata_2[mydata_2$height_seca1 %in% look.for, ]
sex age height_seca1 height_chad1 height_DL weight_alog1
7 F 19 1578 1576 156 50.0
11 F 28 1616 1619 161 65.5
27 M 26 1658 1658 165 69.0
>