For the first one, we have to show that $2^{n-4} \leq c \times 2^{n-10}$ for all $n \geq n_0$.
This is true for any $c \geq 2^6$ as we get by solving the inequality.
For the second one, we have to prove that $f(n) \geq c \times g(n)$ for all $n \geq n_0$
$\implies 2^{n-4} \geq c \times n^{1000}$.
This is true for all $n_0$ when $n - 1000 \log n > 4$. You can get this inequality by doing using the limit definition while comparing terms.
For the third, we have to show $c_1 \times 2^{n-3} \leq 2^{n-4} \leq c_2 \times 2^{n+3}$.
You can find $c_1, c_2$ according to this condition.
Hence, all three are true.