Can I use a Mann-Whitney U Test with a very small sample? I want to compare differences between two independent groups (female and male) when dependent variables are continuous. However, my sample size is very small (N=6). I have done a Mann-Whitney U Test and I am not sure if the results are meaningful given the small sample.

For a 2-sample Wilcoxon Rank Sum test (equivalent to Mann-Whitney U test),
the smallest sample size of each of the two samples is $n_1=n_2=3$
in order for a one-sided test to give significance level 5% or less.
Even then, significance requires complete separation; that is, all
observations in one sample must be smaller than any observation in
the other (and with no tied data). Using R:
wilcox.test(c(5,6,7),c(2,3,4), alt="g")

        Wilcoxon rank sum test

data:  c(5, 6, 7) and c(2, 3, 4)
W = 9, p-value = 0.05
alternative hypothesis: 
 true location shift is greater than 0

That is because ${6 \choose 3} = 20.$
1/choose(6,3)
[1] 0.05

Similarly, for a two-sided test at or below level 5%, the smallest sample sizes are $n_1 = n_2=4.$
wilcox.test(c(5,6,7,8),c(1,2,3,4))

        Wilcoxon rank sum test

data:  c(5, 6, 7, 8) and c(1, 2, 3, 4)
W = 16, p-value = 0.02857
alternative hypothesis: 
 true location shift is not equal to 0

That is because $\frac{2}{{8\choose 4}} = 2/70 =  0.02857.$
2/choose(8,4)
[1] 0.02857143

Also,
wilcox.test(c(5,6,7,8),c(1,2,3))$p.val
[1] 0.05714286

