+118667 There might be an easier way to do this but this is what I have learnt. (I think from Heureka) Thanks Heureka
How many integers n satisfy 0 < n < 60 and 4n=6 (mod 7)
4n=6 (mod 7)
\(4n=6\mod 7\\ 4n=7k+6\\ 4n=8k+4-k+2\\ n=(2k+1)+\frac{2-k}{4}\\ let \;\;a=\frac{2-k}{4}\\ \text{after rearranging }k=2-4a\\ \text{substituting back in}\\ n=2(2-4a)+1+a\\ n=5-7a\\ \text{n is between 0 and 60}\\ n=5,12,19,26,33,40,47,54 \)
So I found 8.
