From tables a 1-tail test for 22 dof lies between 0.001 (3.505) and 0.005 (2.819).
We can produce an approximate linear relationship between the probability p and the t-value.
(2.819-3.505)/(0.005-0.001)=-171.5; p=-171.5t+c where c is a constant to find.
Plug in (t,p)=(0.001,3.505): 3.505=-0.1715+c, c=3.6765.
When p=2.92, 2.92=-171.5t+3.6765, t=0.7565/171.5=0.0044.
The p-value is therefore 0.0044.