Notice that
[tex]2^1=2[/tex]
[tex]2^2=4[/tex]
[tex]2^3=8[/tex]
[tex]2^4=16[/tex]
[tex]2^5=32[/tex]
so that for each power of 2, there is a pattern of period 4. This means that for integers [tex]k\ge0[/tex], each of [tex]2^{4k}[/tex], [tex]2^{4k+1}[/tex], [tex]2^{4k+2}[/tex], and [tex]2^{4k+3}[/tex] have the same units digit.
We can write [tex]50=4(12)+2[/tex], and since [tex]3=4(0)+2[/tex], it follows that [tex]2^{50}[/tex] and [tex]2^3[/tex] share the same units digits. So the units digit of [tex]2^{54}[/tex] is 8.
