Answer
See the detailed answer below.
Work Step by Step
We have 2 wires, and the currents in both of them are equal in magnitude but opposite in direction.
So according to the right-hand rule, the direction of the magnetic field of the first wire (upper wire) at any point upper this wire is out of the page toward you, while the direction of the same wire at any point below this wire is into the page.
By the same approach, the direction of the magnetic field of the second wire (lower wire) at any point upper this wire is into the page, while the direction of the same wire at any point below this wire is out of the page.
At point a, the magnetic field of the upper wire (wire 1) is out of the page, and from the other wire is into the page.
$$\sum B_a=B_1-B_2$$
We know that the magnetic field of a long straight current wire is given by
$$B=\dfrac{\mu_0I}{2\pi d}$$
$$\sum B_a=\dfrac{\mu_0I_1}{2\pi d_1} -\dfrac{\mu_0I_2}{2\pi d_2} $$
where $I_1=I_2=I$;
$$\sum B_a=\dfrac{\mu_0I }{2\pi }\left[ \dfrac{1}{d_1} -\dfrac{1}{ d_2} \right]$$
Plug the known;
$$\sum B_a=\dfrac{(4\pi \times 10^{-7})(10) }{2\pi }\left[ \dfrac{1}{0.02} -\dfrac{1}{ 0.06} \right]$$
$$\sum B_a=(\color{red}{\bf 6.7\times 10^{-5}}\;{\rm T}) \tag{Out of the page}$$
At point b, the two magnetic fields are pointing into the page. So by the same approach,
$$\sum B_b=\dfrac{\mu_0I }{2\pi }\left[ \dfrac{1}{d_1} +\dfrac{1}{ d_2} \right]$$
where $d_1=d_2=d$,
$$\sum B_b=\dfrac{\mu_0I }{2\pi }\left[ \dfrac{2}{d} \right]$$
Plug the known;
$$\sum B_b=\dfrac{(4\pi \times 10^{-7})(10) }{2\pi }\left[ \dfrac{2}{0.02} \right]$$
$$\sum B_b=(\color{red}{\bf 2\times 10^{-4}}\;{\rm T}) \tag{Into the page}$$
At point c, the magnetic field of the lower wire (wire 2) is out of the page, and from the other wire is into the page.
$$\sum B_c=B_2-B_1$$
By the same approach,
$$\sum B_c=\dfrac{\mu_0I }{2\pi }\left[ \dfrac{1}{d_2} -\dfrac{1}{ d_1} \right]$$
Plug the known;
$$\sum B_c=\dfrac{(4\pi \times 10^{-7})(10) }{2\pi }\left[ \dfrac{1}{0.02} -\dfrac{1}{ 0.06} \right]$$
$$\sum B_c=(\color{red}{\bf 6.7\times 10^{-5}}\;{\rm T}) \tag{Out of the page}$$
