The answer by @Dave2e is fine (+1), but I wanted to
give an Answer based mainly on a specific example.

Consider the following fictitious data:

    set.seed(2022)
    x1 = rnorm(30, 350, 50)
    x2 = rnorm(30, 300, 70)

Now do a two sample Welch t test of $H_0: \mu_1=\mu_2$
against $H_a: \mu_1 > \mu_2,$ using `t.test` in R:

    t.test(x1,x2, alt="gr")

            Welch Two Sample t-test

    data:  x1 and x2
    t = 2.6864, df = 55.074, p-value = 0.004764
    alternative hypothesis: 
     true difference in means is greater than 0
    95 percent confidence interval:
     13.8086     Inf
    sample estimates:
    mean of x mean of y 
     344.2034  307.5991 

The P-value of the test is computed by looking in the
upper tail of Student's t distribution with 55.074 degrees
of freedom. [DF is adjusted downward from $n_1+n_2-2=58$ to compensate for the difference
in sample variances.]

    1 - pt(2.6864, 55.074) 
    [1] 0.004764504

[In R, `pt` is a CDF of Student's t distribution.]

The P-value is the area under the density curve to the right of the vertical dotted red line.

[![enter image description here][1]][1]

R code for figure:

    curve(dt(x, 55.074), -4, 4, 
             ylab="Denssity", xlab="t", main=hdr)
     abline(h=0, col="green2")
     abline(v=0, col="green2")
     abline(h= 2.6864, col="red", lwd=2, lty="dotted")
     abline(v= 2.6864, col="red", lwd=2, lty="dotted")


If you do a 2-sided t test, then the P-value is calculated
by looking both in the lower tail below $-2.6864$ and in the upper tail above $2.6864.$  [By using `$`-notation, we show only the P-value.]

    t.test(x1, x2)$p.val
    [1] 0.009528523

This P-value for a 2-sided test is computed as follows:

    pt(-2.6864, 55.074) + 1 - pt(2.6864, 55.074)  
       # left tail + right tail
    [1] 0.009529008

Alternatively, using the symmetry of the t distribution:

    2*pt(-2.6864, 55.074)   $ Double left tail probability 
    [1] 0.009529008

_Note:_ Quantities in the output of the test are rounded slightly
to save space, so there is a tiny discrepancy with the P-values shown just above.

However, if you get confused (easy to do), and ask for the
wrong side, using parameter `alt="less"` in `t.test`, then
you get a nonsense P-value near $1.$

     t.test(x1, x2, alt="less")$p.val
     [1] 0.9952357


 


  [1]: https://i.sstatic.net/MXump.png